IS THERE ONE OR TWO COOLING FANS IS THERE A RELAY

That vehicle has 3 relays ,not just 2 . Two cooling fans .

Cooling Fan Control
The engine cooling fan system consists of two electrical cooling fans and three fan relays. The relays are arranged in a series/parallel configuration that allows the powertrain control module (PCM) to operate both fans together at low or high speeds. The cooling fans and fan relays receive battery positive voltage from the underhood junction block. The ground path is provided at G103.
During low speed operation, the PCM supplies the ground path for the low speed fan relay through the low speed cooling fan relay control circuit. This energizes the cooling fan 1 relay coil, closes the relay contacts, and supplies battery positive voltage from the cool fan 1 fuse through the cooling fan motor supply voltage circuit to the left cooling fan. The ground path for the left cooling fan is through the cooling fan s/p relay and the right cooling fan. The result is a series circuit with both fans running at low speed.
During high speed operation the PCM supplies the ground path for the cooling fan 1 relay through the low speed cooling fan relay control circuit. After a 3-second delay, the PCM supplies a ground path for the cooling fan 2 relay and the cooling fan s/p relay through the high speed cooling fan relay control circuit. This energizes the cooling fan s/p relay coil, closes the relay contacts, and provides a ground path for the left cooling fan. At the same time the cooling fan 2 relay coil is energized closing the relay contacts and provides battery positive voltage from the cool fan 2 fuse on the cooling fan motor supply voltage circuit to the right cooling fan. During high speed fan operation, both engine cooling fans have there own ground path. The result is a parallel circuit with both fans running at high speed.
The PCM commands Low Speed Fans on under the following conditions:
• Engine coolant temperature exceeds approximately 106°C (223°F).
• A/C refrigerant pressure exceeds 1310 kpa (190 psi).
• After the vehicle is shut off if the engine coolant temperature at key-off is greater than 140°C (284°F) and system voltage is more than 12 volts. The fans will stay on for approximately 3 minutes.
The PCM commands High Speed Fans on under the following conditions:
• Engine coolant temperature reaches 110°C (230°F).
• A/C refrigerant pressure exceeds 1655 kpa (240 psi).
• When certain DTCs set.


https://www.youtube.com/watch?v=pI4pH66TdDk

No switch - the radiator cooling fans are controlled by the PCM which receives a signal from the coolant temperature sensor located at the passenger side end of the engine at the lower right.

Usually a bad relay. See this post on GM relays and cooling fans

https://ricksfreeautorepairadvice.com/car-overheating/

Possible bad fuse, relay or switch.

It means you should take your vehicle to a qualified repair shop , at least that's the car makers thought .
A/C Off For Engine Protection
Refer to Cooling System Description and Operation
Cooling Fan Control
The engine cooling fan system consists of 2 electrical cooling fans and 3 fan relays. The relays are arranged in a series/parallel configuration that allows the powertrain control module (PCM) or engine control module (ECM) to operate both fans together at low or high speeds. The cooling fans and fan relays receive battery positive voltage from the underhood junction block. The ground path is provided at G100.
During low speed operation, the PCM/ECM supplies the ground path for the low speed fan relay through the low speed cooling fan relay control circuit. This energizes the cooling fan 1 relay coil, closes the relay contacts, and supplies battery positive voltage from the cool fan 1 maxifuse?® through the cooling fan motor supply voltage circuit to the left cooling fan. The ground path for the left cooling fan is through the cooling fan relay and the right cooling fan. The result is a series circuit with both fans running at low speed.
During high speed operation, the PCM/ECM supplies the ground path for the cooling fan 1 relay through the low speed cooling fan relay control circuit. After a 3 second delay, the PCM/ECM supplies a ground path for the cooling fan 2 relay and the cooling fan relay through the high speed cooling fan relay control circuit. This energizes the cooling fan relay coil, closes the relay contacts, and provides a ground path for the left cooling fan. At the same time the cooling fan 2 relay coil is energized closing the relay contacts and provides battery positive voltage from the cool fan 2 maxifuse?® on the cooling fan motor supply voltage circuit to the right cooling fan. During high speed fan operation, both engine cooling fans have there own ground path. The result is a parallel circuit with both fans running at high speed.
Are the radiator fans coming on ? You mite take it an have it checked for DTC'S - diagnostic trouble code's .

ENGINE HOT - AC OFF
Cooling System Description and Operation

you must have a cooling system problem of some sort !

Do the cooling fans come on when A/C is switched on ? Fan's should come on ! Does your vehicle have two or three cooling fan's ?
Cooling Fan Control - Two Fan System
The engine cooling fan system consists of 2 puller type electrical cooling fans and 3 fan relays. The relays are arranged in a series parallel (S/P) configuration that allows the engine control module (ECM) to operate both fans together at low or high speeds. The cooling fans and fan relays receive battery positive voltage from the underhood fuse block. The ground path is provided at G104.
During low speed operation, the ECM supplies the ground path for the low speed fan relay through the low speed cooling fan relay control circuit. This energizes the low speed fan relay coil, closes the relay contacts, and supplies battery positive voltage from the low fan fuse through the cooling fan motor supply voltage circuit to the left cooling fan. The ground path for the left cooling fan is through the cooling fan S/P relay and the right cooling fan. The result is a series circuit with both fans running at low speed.
During high speed operation the ECM supplies the ground path for the low speed fan relay through the low speed cooling fan relay control circuit. After a 3 second delay, the ECM supplies a ground path for the high speed fan relay and the cooling fan S/P relay through the high speed cooling fan relay control circuit. This energizes the cooling fan S/P relay coil, closes the relay contacts, and provides a ground path for the left cooling fan. At the same time, the high speed fan relay coil is energized closing the relay contacts, and provides battery positive voltage from the high fan fuse on the cooling fan motor supply voltage circuit, to the right cooling fan. During high speed fan operation, both engine cooling fans have their own ground path. The result is a parallel circuit with both fans running at high speed.
The ECM commands the low speed cooling fans ON under the following conditions:
• Engine coolant temperature exceeds approximately 94.5°C (202°F).
• A/C refrigerant pressure exceeds 1447 kPa (210 psi).
• After the vehicle is shut OFF, if the engine coolant temperature at key-off is greater than 101°C (214°F), the low speed fans will run for a minimum of 60 seconds. After 60 seconds, if the coolant temperature drops below 101°C (214°F), the fans will shut OFF. The fans will automatically shut OFF after 3 minutes, regardless of coolant temperature.
The ECM commands the high speed fans ON under the following conditions:
• Engine coolant temperature exceeds approximately 104.25°C (220°F).
• A/C refrigerant pressure exceeds approximately 1824 kPa (265 psi).
• When certain DTCs set
At idle and very low vehicle speeds the cooling fans are only allowed to increase in speed, if required. This ensures idle stability by preventing the fans from cycling between high and low speed.
Cooling

Having a qualified professional technician check it out would be your best bet ! Hooking up a factory or professional type scanner an check data input's an DTC'S - diagnostic trouble codes .

Diagnostic Starting Point - Engine Cooling
Begin the system diagnosis with the diagnostic system check. Refer to Diagnostic System Check - Vehicle . The Diagnostic System Check - Vehicle will provide the following information:
• The identification of the control modules which command the system
• The ability of the control modules to communicate through the serial data circuits
• The identification of any stored DTCs and their status
The use of the Diagnostic System Check - Vehicle will identify the correct procedure for diagnosing the system and where the procedure is located.

DTC P0480: Cooling Fan Relay 1 Control Circuit
DTC P0481: Cooling Fan Relay 2 Control Circuit
DTC P0480: Cooling Fan Relay 1 Control Circuit
DTC P0481: Cooling Fan Relay 2 Control Circuit
DTC P0691: Cooling Fan Relay 1 Control Circuit Low Voltage
DTC P0692: Cooling Fan Relay 1 Control Circuit High Voltage
DTC P0693: Cooling Fan Relay 2 Control Circuit Low Voltage
DTC P0694: Cooling Fan Relay 2 Control Circuit High Voltage
DTC P1258: Engine Coolant Overtemperature - Protection Mode Active
DTC P2600: Auxiliary Coolant Pump Relay Control Circuit
DTC P2601: Auxiliary Coolant Pump Performance
DTC P2602: Auxiliary Coolant Pump Relay Control Circuit Low Voltage
DTC P2603: Auxiliary Coolant Pump Relay Control Circuit High Voltage

Your vehicle cooling fan's are controlled by three relay's , couple of fuse's an the PCM - engine computer . The engine coolant temp. sensor is a input to the PCM , when engine temp get's to 212 the PCM will turn on the cooling fans in low speed . Checking to see what the actual temp is with a scan tool an a infrared thermometer at the thermostat housing ,an looking up the specification's in a service repair manual is how to diagnose . Not guessing an replacing parts . Plus learning how the cooling fan's work .
Relay Driven Dual Cooling Fan Diagnostics Reading factory service info as to how they work also would be a good idea .

Cooling Fan Control - Two Fan System
The engine cooling fan system consists of 2 puller type electrical cooling fans and 3 fan relays. The relays are arranged in a series parallel (S/P) configuration that allows the engine control module (ECM) to operate both fans together at low or high speeds. The cooling fans and fan relays receive battery positive voltage from the underhood fuse block. The ground path is provided at G104.
During low speed operation, the ECM supplies the ground path for the low speed fan relay through the low speed cooling fan relay control circuit. This energizes the low speed fan relay coil, closes the relay contacts, and supplies battery positive voltage from the low fan fuse through the cooling fan motor supply voltage circuit to the left cooling fan. The ground path for the left cooling fan is through the cooling fan S/P relay and the right cooling fan. The result is a series circuit with both fans running at low speed.
During high speed operation the ECM supplies the ground path for the low speed fan relay through the low speed cooling fan relay control circuit. After a 3 second delay, the ECM supplies a ground path for the high speed fan relay and the cooling fan S/P relay through the high speed cooling fan relay control circuit. This energizes the cooling fan S/P relay coil, closes the relay contacts, and provides a ground path for the left cooling fan. At the same time, the high speed fan relay coil is energized closing the relay contacts, and provides battery positive voltage from the high fan fuse on the cooling fan motor supply voltage circuit, to the right cooling fan. During high speed fan operation, both engine cooling fans have their own ground path. The result is a parallel circuit with both fans running at high speed.
The ECM commands the low speed cooling fans ON under the following conditions:
• Engine coolant temperature exceeds approximately 94.5°C (202°F).
• A/C refrigerant pressure exceeds 1447 kPa (210 psi).
• After the vehicle is shut OFF, if the engine coolant temperature at key-off is greater than 101°C (214°F), the low speed fans will run for a minimum of 60 seconds. After 60 seconds, if the coolant temperature drops below 101°C (214°F), the fans will shut OFF. The fans will automatically shut OFF after 3 minutes, regardless of coolant temperature.
The ECM commands the high speed fans ON under the following conditions:
• Engine coolant temperature exceeds approximately 104.25°C (220°F).
• A/C refrigerant pressure exceeds approximately 1824 kPa (265 psi).
• When certain DTCs set
At idle and very low vehicle speeds the cooling fans are only allowed to increase in speed, if required. This ensures idle stability by preventing the fans from cycling between high and low speed.

A/C Off For Engine Protection
Refer to Cooling System Description and Operation

DTC P1258: Engine Coolant Overtemperature - Protection Mode Active.
This is something you need to take to a qualified repair shop .
The engine cooling fan system consists of 2 electrical cooling fans and 3 fan relays. The relays are arranged in a series/parallel configuration that allows the powertrain control module (PCM) or engine control module (ECM) to operate both fans together at low or high speeds. The cooling fans and fan relays receive battery positive voltage from the underhood junction block. The ground path is provided at G100.
During low speed operation, the PCM/ECM supplies the ground path for the low speed fan relay through the low speed cooling fan relay control circuit. This energizes the cooling fan 1 relay coil, closes the relay contacts, and supplies battery positive voltage from the cool fan 1 maxifuse® through the cooling fan motor supply voltage circuit to the left cooling fan. The ground path for the left cooling fan is through the cooling fan relay and the right cooling fan. The result is a series circuit with both fans running at low speed.
During high speed operation, the PCM/ECM supplies the ground path for the cooling fan 1 relay through the low speed cooling fan relay control circuit. After a 3 second delay, the PCM/ECM supplies a ground path for the cooling fan 2 relay and the cooling fan relay through the high speed cooling fan relay control circuit. This energizes the cooling fan relay coil, closes the relay contacts, and provides a ground path for the left cooling fan. At the same time the cooling fan 2 relay coil is energized closing the relay contacts and provides battery positive voltage from the cool fan 2 maxifuse® on the cooling fan motor supply voltage circuit to the right cooling fan. During high speed fan operation, both engine cooling fans have there own ground path. The result is a parallel circuit with both fans running at high speed.

The engine cooling fan system is controlled by the body control module (BCM) and the powertrain control module (PCM) or engine control module (ECM). The BCM performs the calculations as to how long, when and what speed the cooling fans should turn on. The BCM then sends a class 2 message to the PCM/ECM to engage the cooling fan relays. If there is a malfunction with the BCM, the PCM/ECM will control the engine cooling fans independently. The engine cooling system consists of 2 electrical cooling fans and 3 fan relays. The relays are arranged in a series/parallel configuration that allows the PCM/ECM to operate both fans together at low or high speeds. The cooling fans and fan relays receive battery positive voltage from the underhood accessory wiring junction block. The ground path is provided at G100.
During low speed operation, the PCM/ECM supplies the ground path for the low speed fan relay through the low speed cooling fan relay control circuit. This energizes the cooling fan 1 relay coil, closes the relay contacts, and supplies battery positive voltage from the cool fan 1 fuse through the cooling fan motor supply voltage circuit to the left cooling fan. The ground path for the left cooling fan is through the cooling fan 2 relay and the right cooling fan. The result is a series circuit with both fans running at low speed.
During high speed operation the PCM/ECM supplies the ground path for the cooling fan 1 relay through the low speed cooling fan relay control circuit. After a 3 second delay, the PCM/ECM supplies a ground path for the cooling fan 3 or S/P relay and the cooling fan 2 relay through the high speed cooling fan relay control circuit. This energizes the cooling fan 2 relay coil, closes the relay contacts, and provides a ground path for the left cooling fan. At the same time the cooling fan 2 relay coil is energized closing the relay contacts and provides battery positive voltage from the cool fan 2 fuse on the cooling fan motor supply voltage circuit to the right cooling fan. During high speed fan operation, both engine cooling fans have there own ground path. The result is a parallel circuit with both fans running at high speed.
The BCM and PCM/ECM command Low Speed Fans on under the following conditions:
?€¢
Engine coolant temperature exceeds approximately 106?°C (223?°F).

?€¢
A/C refrigerant pressure exceeds 1 310 kPa (190 psi).

?€¢
After the vehicle is shut off if the engine coolant temperature at key-off is greater than 140?°C (284?°F) and system voltage is more than 12 volts. The fans will stay on for approximately 3 minutes.

The BCM and PCM/ECM command High Speed Fans on under the following conditions:
?€¢
Engine coolant temperature reaches 110?°C (230?°F).

?€¢
A/C refrigerant pressure exceeds 1 655 kPa (240 psi).

?€¢
When certain DTCs set.

The three relays are located in the under hood fuse / relay box ! You need to have it checked for DTC'S -diagnostic trouble codes ! An you need a GM Tech 2 scan tool !
This diagnostic procedure supports the following DTCs:
?€¢
DTC P0480 Cooling Fan 1 Relay Control Circuit

?€¢
DTC P0481 Cooling Fan 2 and 3 or S/P Relay Control Circuit

?€¢
DTC P0691 Cooling Fan 1 Relay Control Circuit Low Voltage

?€¢
DTC P0692 Cooling Fan 1 Relay Control Circuit High Voltage

?€¢
DTC P0693 Cooling Fan 2 and 3 or S/P Relay Control Circuit Low Voltage

?€¢
DTC P0694 Cooling Fan 2 and 3 or S/P Relay Control Circuit High Voltage

1. Install a scan tool.
2. Turn ON the ignition, with the engine OFF.
3. With a scan tool, command the Fans Low Speed ON and OFF.

Do the low speed engine cooling fans turn ON and OFF with each command?
Go to Step 3
Go to Step 4

3

Important:: A 3 second delay occurs before the powertrain control module (PCM)/engine control module (ECM) changes the cooling fan speed.
With a scan tool, command the Fans High Speed ON and OFF.
Do the high speed engine cooling fans turn ON and OFF with each command?

The engine cooling fan system consists of 2 electrical cooling fans and 3 fan relays. The relays are arranged in a series/parallel configuration that allows the powertrain control module (PCM) to operate both fans together at low or high speeds. The cooling fans and fan relays receive battery positive voltage from the underhood accessory wiring junction block. The ground path is provided at G113. The relays are located in the underhood fuse / relay box .
So ,what's the problem Paul , car overheating ? Fans not working ?
During low speed operation, the PCM supplies the ground path for the low speed fan relay through the low speed cooling fan relay control circuit. This energizes the cooling fan 1 relay coil, closes the relay contacts, and supplies battery positive voltage from the cool fan 1 fuse through the cooling fan motor supply voltage circuit to the right cooling fan. The ground path for the right cooling fan is through the cooling fan 2 relay and the left cooling fan. The result is a series circuit with both fans running at low speed.
During high speed operation the PCM supplies the ground path for the cooling fan 1 relay through the low speed cooling fan relay control circuit. After a 3-second delay, the PCM supplies a ground path for the cooling fan 2 relay and the cooling fan 3 relay through the high speed cooling fan relay control circuit. This energizes the cooling fan 2 relay coil, closes the relay contacts, and provides a ground path for the right cooling fan. At the same time the cooling fan 3 relay coil is energized closing the relay contacts and provides battery positive voltage from the cool fan 2 fuse on the cooling fan motor supply voltage circuit to the left cooling fan. During high speed fan operation, both engine cooling fans have there own ground path. The result is a parallel circuit with both fans running at high speed.
The PCM commands Low Speed Fans on under the following conditions:
?€¢
Engine coolant temperature exceeds approximately 106?°C (223?°F).

?€¢
When the A/C is requested and the ambient temperature is more than 50?°C (122?°F).

?€¢
A/C refrigerant pressure exceeds 1310 kPa (190 psi).

?€¢
After the vehicle is shut off if the engine coolant temperature at key-off is greater than 140?°C (284?°F) and system voltage is more than 12 volts. The fans will stay on for approximately 3 minutes.

The PCM commands High Speed Fans on under the following conditions:
?€¢
Engine coolant temperature reaches 110?°C (230?°F).

?€¢
A/C refrigerant pressure exceeds 1655 kPa (240 psi).

?€¢
When certain DTCs set.

So