If the gauge reads full all the time then some of the possible problems are: •A poor or broken connection between the sender and the gauge •A broken resistance wire in the sender sending a faulty signal •The tank is not grounded to the chassis which means the sender may not be grounded either.
To figure out what the problem is you should first remove the wire from the terminal on the sender and ground it directly to your vehicle’s chassis. If the gauge now reads empty then the sender or the tank are not grounded properly or it could just be that the sender has gone bad.
If this does not produce results, ground a test lead and and touch it to the terminal on the back of the gauge. It is often marked with a red tag. If the gauge now goes to empty then you know that the wire between the sender and the dash gauge is loose or broken and needs to be replaced.
One final test you can run is to remove the sender from the tank and connect it to an ohmmeter. One lead goes to the sender terminal and the other connects to the sender housing. Once you have it hooked up simply move the float arm and check the resistance measured by the meter. It should vary from 0 to 30 ohms most likely or at whatever range your sender unit has. As long as the ohms are changing you know it isn’t the sender that has gone bad.