Switch off the ignition. Disconnect the wire from the sender unit on the fuel tank, tape the end of the lead with electrical tape to prevent shorting, remove the sender unit, and check the float for freedom of movement. Connect an analog ohmmeter to the terminal on the sender unit and the body of the sender unit, which is grounded by the fastening screws when the sender unit is installed on the fuel tank, and slowly move the float up and down. The resistance should vary smoothly. If that is the case, the sender unit is OK. If not, the sender unit is defective and will have to be replaced. I found that the sender unit on my Healey had been installed backwards. The float should face the front of the car for the gauge to indicate properly. Also remake all electrical connections. Clean the fastening screws for the sender unit, the tapped holes on the tank flange, and use serrated washers under the nuts on the sender unit and the gauge. If that does not help, then the gauge is the problem and will have to be replaced. I always switch on the ignition and watch the fuel gauge while I am filling the tank. If the fuel gauge shows an increasing fuel level ans the tank is filled and shows full wheh the tank is full, then everything is operating as it should. Nevertheless, I never trust fuel gauges and carry two, filled, five-liter, gas cans in the car at all times.