I have no experience with the specifics of the 100 fuel gauge. However, the gauge system is almost certainly Smiths/British-Jaeger magnetic.
On magnetic gauge systems it is imperative that the gauge case has a good ground and that the tank has a good ground. The sending units typically operated from low resistance = empty to high resistance = full. With the sending unit out of the car you can test the sending unit with a multimeter. Connect one probe to the sender flange or ground terminal, connect the other probe to the insulated sender terminal. Moving the float arm up and down should produce a resistance change... probably in the range of 0 to 90 Ohms. If you see a resistance change that goes to "infinite" somewhere along the travel, the sender resistance windings have an open. Repair is typically by replacement.
If you want to check the gauge, at the sending unit locate the green/black wire. With the ignition in the run position, disconnect the green/black wire from the sending unit. The gauge should go to (above) full. Now touch the bare end of the green/black wire to chassis ground (on the car, not the tank or sender). The gauge should go to (below) empty. If that doesn't happen, check that the gauge case has a good ground and repeat the test. If the gauge still doesn't respond you have a gauge issue to sort out.
All of this assumes you are getting 12V to the "B" terminal on the back of the gauge and that the green/black sending unit wire is securely attached to the gauge's "T" terminal.