84 bonneville fuel gage

You need to isolate what the problem is. First, check the power supply/ fuse for the instruments, ensure the gauge has a supply. Check the earthing at both the tank end and the gauge (body). With a meter, you should see 12V. (or maybe less, if the Bonneville has a regulator on the instruments, I don't specifically know the vehicle). This should appear between one of the rear terminals of the gauge and the case, when the ignition is on. If present there, check it is still there when checked between that terminal and another earth point on the car's metalwork.
The other terminal on the gauge is the transmitter termination. If the power is present, removing the transmitter wire should cause the gauge to either go full scale, or not move at all. Use a piece of wire to short this terminal to ground, the meter should do the opposite to the previous test. If no movement, the gauge is faulty. Replace.
At the tank end, you should find the transmitter unit. It should have a single wire connected to a terminal. Remove this. With aan ohmmeter, check for a resistance reading between this terminal and ground. If no meter, turn on the ignition with this wire disconnected, the gauge should do the same as it did when the wire was removed behind the gauge. If it does, short the removed wire of the transmitter to ground, the gauge should do the same as the short test at the gauge, If not, the wire is broken or shorted somewhere between the gauge and transmitter.
If the gauge moves as before when testing from the transmitter wire, most probably the transmitter is faulty.
Too hard? Leave it to the experts...!?! ;-]