My 1996 cadillac eldo fan low speed only

If you make a jumper wire and jump the load side of the relay and the fans work, it might be the relay or it might be the control side of the relay not getting the signal from the temperature switch. If you jump the load side and the fans don't work it's either the fan motors or a wiring issue between the relay and the fans.

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.

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 Fan Control Module or FMC is the long black relay located underneath your coolant bulb, It is mounted onto a bracket on the drivers side shock tower, to test your fans you can take off the temp sensor located on the drivers side tank on your radiator, jump the terminals and the fan should come on in low speed, turn your ignition to the on position and jump them and it should turn onto high speed.
The best solution is to wire the fan to a 12v switched power source on high speed.

Well I'm sure there are kits to wire up electric fans on cars that are not designed for one.
You would need a relay and something to turn the relay on. A coolant sensor won't do the trick, the sensor is what tells the computer the engine temp, and the computer decides when to ground the fan relay.
You would need a temp switch that is designed to close at say 220 degrees to ground or power the fan relay.
The fan motor would have ground and power wires.

Try to flush and fill with new fluid to get the passageways free of sediment.

Or, try to see if the fans are coming on at the right speed at operating temperature. May require new fans/relays/wiring to fix this problem.

I have a 1997 Cadillac Deville that was overheating its Northstar engine and it required service amounting to about $700.00 or so from an auto electric shop, but afterwards it ran cooler.

Good luck on this repair.

In the fuse/relay box under the hood in front of the battery are 3 fan relays. 1 for low speed, and 2 for high speed. 1 of high speed is back up. check the relays first.
B3 CHECK FUSES

• Key OFF.
• Check the 10A RELAYS fuse located in the interior fuse junction panel and the 65A RAD FAN fuse located in the main fuse junction panel. (engine compartment)

pLease rate as fixya if this helps. good luck

I assume you mean engine/radiator cooling fan. You have 3 relays in the power box under the hood by the battery. They are labeled, one low speed fan relay and 2 high speed fan relays. One of the high speed relays is a default back up relay if the others fail, it will go to high speed all the time. Maybe you have a bad cooling fan. Buy in Ebay cheap.

when you first start the vehicle the fans whill cycle automatically. when the engine reaches temp the fans should kick on if they don't it is most like that you have either a weak relay or a loose wire very seldom would it be a severe ecm malfunction. please rate this solution

Hello, look on the left (driver side) front of the engine, you will see at the end of the closest to you, on the cylinder head, a pulley. This pulley runs your water pump, by a belt connection. Check and see if that belt is on.
If you are adding water, you should have it pressure tested, as it could be the water pump(which takes a special tool to replace) or a bad head gasket.