Fuel gage works correctly sometime - 1997 Jaguar XK8

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.

To troubleshoot, I need year--make--model, vehicle sold in the US.
I'd check the coolant temp sensor and wiring circuits. The same thing for fuel gage sending unit. Sometimes for the fuel gage sending unit, I get a couple of resistors one represents empty, the other represents full. If the gage reacts properly then the problem should be the sending unit in the gas tank.

Check the work. The fuel level wiring might not have gotten plugged in. Also, if the fuel pump was a pain to get out for whatever reason, the wiring on the inside might have gotten broken off or the arm that holds the float got bent. Lastly, it doesn't happen a lot anymore but sometimes the float just sinks and stays there. The newer floats are made of foam so they tend to last.

I am no expert, But:

The sending units could be dirty, both wires could be touching where insulation has failed if both are in same wiring harness, or both sending units have went bad.

Check fuel gauge sensor , Code on computer

sounds Like You HAve Ground Problem Clean the CABLE Goin to Your Battery And then Look On YouTube to See How They Do It Ok

Hello
This problem is caused by only thing, it is a defective fuel level sending unit inside the fuel tank. To replace this part requires the fuel tank be removed from the vehicle.

Probably fuel pump about to go out. This happened to me and about 2 mo.s later, fuel pump had to be replaced. Bad thing is, it is in the the fuel tank.

check your fuel pump wireing

Problem may be with the level sending unit, which is part of the fuel pump assembly in the fuel tank. You can check this with a good code reader that will give you live data from this unit and compare it with what the gauge is saying. If they don't match, you can try a good quality fuel system cleaner to see if that solves the problem. If they do match, then the problem is probably still in your instrument panel (IP) or engine computer.