The fuel gage does not work ('02 Cabrio, 2.0). The cluster is working. Would the fuel level sensor be the next thing in the T/S process? And does the pump have to be R&R'd to replace the sensor?

More than likely a broken wire, corroded connector or a chafed wire.

https://www.carproblemzoo.com/chevrolet/suburban/2003/2003-chevrolet-suburban-electrical-system-problems.php This site may help you find your problem. There are many different problems with the Suburban dashes.

Replace the instrument cluster . GM had stepper motor issues 2003 to 2006 . Pin out won't help you , The info for the instrument cluster gauges come's over class 2 serial data buss (network) from the PCM - engine computer . Do you know what GM class 2 data network is ? All gauge info comes over one wire from the PCM .
How to repair GM Instrument Cluster Speedometer Gauge Stepper
Buick Class 2 Operation Diagnosis 1998

Hooking up a Tech 2 scan tool an checking for code's an data to the instrument cluster would be the correct diagnostic procedure . But you wouldn't know that , not being a Chevy technician . Not having factory service repair info. manual .

Speedometer
The IPC displays the vehicle speed based on the information from the PCM. The PCM calculates the vehicle speed from the vehicle speed sensor (VSS) circuit. The IPC receives a class 2 message from the PCM indicating the vehicle speed. The PCM also calculates the vehicle speed based on the wheel reference vehicle speed class 2 message from the EBCM. The PCM uses the vehicle speed information from the EBCM as a backup. The IPC displays the vehicle speed information from the EBCM when the PCM detects a malfunction in the vehicle speed sensor circuit.
The speedometer defaults to 0 km/h (0 mph) if the IPC detects a loss of class 2 communications with both the PCM and the EBCM.

Engine Coolant Temperature (ECT) Gage
The IPC displays the engine coolant temperature on the analog ECT gage as determined by the PCM. The PCM monitors the signal circuit of the engine coolant temperature sensor. The IPC receives a class 2 message from the PCM indicating the engine coolant temperature. The IPC illuminates the check gages indicator when a high engine coolant temperature condition exists. The engine coolant temperature gage defaults to 75°C (160°F) or below when one of the following conditions occur:
• The PCM detects a malfunction in the engine coolant temperature sensor signal circuit.
• The IPC detects a loss of class 2 communication with the PCM.
For additional informatin on the engine cooling system, refer to Cooling System Description and Operation in Engine Cooling.
Engine Oil Pressure (EOP) Gage
The IPC displays the engine oil pressure on the analog EOP gage as determined by the PCM. The PCM monitors the signal circuit of the engine oil pressure sensor. When the engine oil pressure sensor resistance is high, the engine oil pressure is high. When the engine oil pressure sensor resistance is low, the engine oil pressure is low. The IPC receives a class 2 message from the PCM indicating the engine oil pressure. The IPC illuminates the check gages indicator when a low oil pressure condition exists. The engine oil pressure gage defaults to 0 kPa (0 psi) when the following condition occurs:
• The PCM detects a malfunction in the engine oil pressure sensor signal circuit.
• The IPC detects a loss of class 2 communication with the PCM.
Fuel Gage
The IPC displays the fuel level on the analog fuel gage as determined by the PCM. The PCM monitors the signal circuit of the fuel level sensor. When the fuel level sensor resistance is high, the fuel gage indicates full. When the fuel level sensor resistance is low, the fuel gage indicates empty. The IPC receives a class 2 message from the PCM indicating the filtered fuel level percent. The PCM uses 2 filters for the fuel level percent. The slow filter is used during normal operation. The fast filter is used when the engine is just started or when the vehicle is in Park or Neutral. The fast filter allows the fuel gage to reach the current fuel level quickly. The fuel gage defaults to empty when the following conditions occur:
• The PCM detects a malfunction in the fuel level sensor circuit. Refer to Diagnostic System Check - Instrument Cluster .
• The IPC detects a loss of class 2 communications with the PCM.
Reviewing the fuel system description will further explain how the system functions. Refer to:
• Fuel System Description in Engine Controls - 4.3L
• Fuel System Description in Engine Controls - 4.8L, 5.3L, and 6.0L.

Could be the stepper motor in the instrument cluster . GM instrument cluster had bad stepper motors . 2003 to 2006
How to repair GM Instrument Cluster Speedometer Gauge Stepper

Every light lit on the instrument cluster , could be data network problem . Do you know what a serial data network is , class 2 or GMLAN ? Hooking up a professional or factory scan tool to view sensor data to ECM - engine computer .
Fuel Gage
The instrument panel cluster (IPC) displays the fuel level as determined by the engine control module (ECM). The IPC receives a serial data message from the ECM indicating the fuel level percent. The fuel gage defaults to empty if:
• The ECM detects a malfunction in the fuel level sensor circuit.
• The IPC detects a loss of serial data communications with the ECM.
When the fuel level is less than a pre-determined value, the IPC illuminates the low fuel indicator.

First off you would need to know from where an how this data get's to the instrument cluster , Computers involved ( control module's ) etc... serial data network - how the computers (modules ) communicate . Special tool's involved in testing this data - factory or professional scan tool - to view data from sensor's - temp sensor , fuel level sending unit in the fuel tank . Both of the these sensors are input's to the PCM/ECM - engine computer , which shares this info to other module's which need this info. The GMLAN serial data network is the data network which does this .
The instrument cluster has a microprocessor inside which view's this data an controls stepper motors to drive the gauge need .
Not working correctly or not at all can becaused by any number of thing's . The instrument cluster could have DTC'S - diagnostic trouble code's stored . Auto part stores can not read these code's or BCM code's . .
Engine Coolant Temperature Gage
The engine control module (ECM) calculates the engine coolant temperature as determined by the coolant temperature sensor. The ECM sends the engine coolant temperature to the body control module (BCM) via the serial data circuit. The instrument panel cluster (IPC) displays the engine coolant temperature when the BCM sends a serial data message to the IPC indicating the engine coolant temperature. The engine coolant temperature gage defaults to 0° or below if:
• The ECM detects a malfunction in the engine coolant temperature sensor circuit.
• The IPC detects a loss of serial data communications with the BCM.
• The BCM detects a loss of serial data communications with the ECM.
Fuel Gage
The engine control module (ECM) sends the fuel level percent to the BCM via the serial data circuit. The IPC displays the fuel level as received from the BCM. The fuel gage defaults to E (empty) if:
• The ECM detects a malfunction in the fuel level sensor circuit.
• The IPC detects a loss of serial data communications with the BCM.
• The BCM detects a loss of serial data communications with the ECM.
When the fuel level is less than a pre-determined value, the Low Fuel indicator message illuminates.

Your best bet , take your vehicle to a qualified repair shop.

Yes the fuel tank has to come out to change the fuel pump. But are you sure that is the problem ? Your vehicle has a Fuel Pump Flow Control Module (electronic's ) Or is it just your fuel level sensor you want to replace ? And to your question of if the fuel level sensor is bad will the car shut down if the gage says it is emty but it is not? No ,this will not shut down the vehicle. You probably have no idea of the complexity of the electronic's involved an the thing's that can cause the gauge not to work .
Fuel Gage
The instrument panel cluster (IPC) displays the fuel level as determined by the ECM. The IPC receives a serial data message from the ECM indicating the fuel level percent. The fuel gage defaults to empty if:
• The ECM detects a malfunction in the fuel level sensor circuit.
• The IPC detects a loss of serial data communications with the BCM
• The BCM detects a loss of serial data communications with the ECM
When the fuel level is less than a pre-determined value, the low fuel indicator illuminates in the IPC.
Unless you have a factory or professional type scan tool your better off taking your vehicle to a qualified repair shop.

Fuel Gage Inaccurate or Inoperative
Circuit/System Description
The fuel level sender changes resistance based on the fuel level. The engine control module (ECM) monitors the signal circuit of the fuel level sender to determine fuel level. When the fuel tank is full, the sender resistance is low and the ECM senses a low signal voltage. When the fuel tank is empty, the sender resistance is high and the ECM senses a high signal voltage. The ECM uses the signal circuit of the fuel level sender in order to calculate the remaining fuel level percent in the tank. The ECM sends the fuel level message via the serial data circuit to the body control module (BCM). The BCM sends the fuel level percent to the instrument panel cluster (IPC) via the serial data circuit for display on the fuel gage.

Circuit
Short to Ground
High Resistance
Open
Short to Voltage
Signal Performance
Fuel Level Sensor Signal
P0462
1
P0463, P0464
P0463
P0461
Fuel Level Sensor Low Reference
--
1
P0463, P0464
P0463
P0461
1. Fuel Gage Inaccurate or Inoperative

Do you know what a DTC is ? diagnostic trouble code !

Have the vehicle check for DTC'S - diagnostic trouble codes ! The sending unit is an input to the PCM - engine computer . The PCM sends this info to the instrument cluster over class 2 serial data network . Do you know anything about class 2 communication's network . The ideal way to diagnose a problem like this , check for codes , view data on scan tool . Buick Class 2 Operation Diagnosis 1998

Fuel Gage
The instrument panel cluster (IPC) displays the fuel level as determined by the engine control module (ECM). The IPC receives a serial data message from the ECM indicating the fuel level percent. The fuel gage defaults to empty if:
• The ECM detects a malfunction in the fuel level sensor circuit.
• The IPC detects a loss of serial data communications with the ECM.
When the fuel level is less than a pre-determined value, the IPC illuminates the low fuel indicator.

DTC P0463

Install a scan tool.
Turn the ignition ON, with engine OFF.
With the scan tool, observe one of the following fuel level parameters:
• Fuel Level Sensor parameter in the PCM Enhanced EVAP data list.
• Fuel Level Sensor parameter in the PCM EVAP data list - 4.2L only.
Does the scan tool indicate that the Fuel Level Sensor parameter is less than the specified value?

It's not a fuse problem , fuel sending unit in side the fuel tank is bad or the gauge itself is . Your best bet , have it diagnosed by a qualified repair shop .
The fuel level sending unit in the gas tank is a input to the PCM - engine computer . The PCM shares this fuel level info to the instrument cluster over the class 2 serial data network . If a fuse was bad the whole instrument cluster would be out .

Fuel Gage
The instrument panel cluster (IPC) displays the fuel level as determined by the powertrain control module (PCM). The IPC receives a class 2 message from the PCM indicating the fuel level volume. The fuel gage defaults to E (empty) if:
• The PCM detects a malfunction in the fuel level sensor circuit.
• The IPC detects a loss of class 2 communications with the PCM.
When the fuel level is less than 14 percent, the low fuel indicator illuminates.

At the dealer we would hook up the factory scan tool to see if the info from the PCM is getting to the instrument cluster . How to test fuel gauge tank sending unit P0463 GM

Fuel Gage
The IPC displays the fuel level as determined by the PCM. The IPC receives a class 2 message from the PCM indicating the fuel level percent. The fuel gage defaults to empty if:
• The PCM detects a malfunction in the fuel level sensor circuit.
• The IPC detects a loss of class 2 communications with the PCM.
When the fuel level is less than a pre-determined value, the low fuel indicator illuminates.

Hooking up a professional or factory scanner an checking input data to the PCM from the sending unit inside the fuel tank ,viewing the information sent to the IPC , Checking for diagnostic trouble code's .
DTC P0461
DTC P0462
Circuit Description
The fuel level sender changes resistance based on fuel level. The PCM monitors the signal circuit of the fuel level sender in order to determine fuel level. When the fuel tank is full, the sender resistance is high and the PCM senses a high signal voltage. When the fuel tank is empty, the sender resistance is low and the PCM senses a low signal voltage. The PCM uses the signal circuit of the fuel level sender in order to calculate the total remaining fuel percentage in the tank. The PCM sends the fuel level percent via the class 2 serial data circuit to the instrument cluster in order to control the fuel gage. The fuel level information is also used for misfire and EVAP diagnostics.

Install a scan tool.
Turn the ignition ON, with the engine OFF.
With a scan tool, observe the Fuel Tank Level Remaining parameter in the PCM data list.
Does the scan tool indicate that the Fuel Tank Level Remaining parameter is less than the specified value?
1%

No DTC'S - diagnostic trouble code's stored ,use this diagnostic procedure
Fuel Gage Inaccurate or Inoperative
• Refer to Fuel Level Specifications in order to verify the correct fuel level sensor readings. The Fuel Tank Level Remaining parameter is available in the scan tool in the PCM data list.
Test Description
The numbers below refer to the step numbers on the diagnostic table.
This step tests for a high resistance in the signal circuit and the low reference circuit of the fuel level sensor.
DTCs will be set in the PCM when you perform this diagnostic table.
Step
Action
Value(s)
Yes
No
Schematic Reference: Instrument Cluster Schematics
1
Did you perform the Instrument Cluster Diagnostic System Check?
--
Go to Step 2
Go to Diagnostic System Check - Instrument Cluster
2
Disconnect C104.
Connect the J 33431-C Signal Generator and Instrument Panel Tester between the signal circuit of the fuel level sensor and the low reference circuit of the fuel level sensor on the male terminal side.
Turn the ignition ON, with the engine OFF.
Important: Verify the J 33431-C resistance settings with a DMM.
Vary the resistance on the J 33431-C from 40-250 ohms.
Refer to Fuel Level Specifications in order to convert from resistance to fuel gage display.
Does the fuel gage display the correct fuel level?

How to test fuel gauge tank sending unit P0463 GM

Often a faulty cluster. Changing out the fuel level sensor requires you replace the whole fuel sensor assembly along with the fuel pump....in the fuel tank...both options expensive,.

I believe BBA remanufactures the clusters...other than that, dealership part..