Most fuel gauges send a voltage through the gauge to the sending unit. The sending unit works with a wiper arm that varies with resistance to ground. If you take the wire off the sender and short the wire to ground the gauge should read full. If it doesn't, there may be a short or open in the wire from the gauge. If it does the gauge is probably good. If you can pull the sender out of the tank then attach an ohmmeter one side to the stud the wire came off of, the other to the metal or second stud then swing the float from one end to the other. The ohm reading should be smooth from one end of the meter to the other. If not the wire wound resistor the float arm varies may be bad. It may be tough to check the sender resistance while still in the tank unless you can raise and lower the float arm through the filler neck.