1991 Pontiac Firebird fuel guage

Pretty certain it should read empty in the OFF position. Easy way to test the sending unit is to unplug it, its near the fuel tank. Once unplugged, turn ignition on. If the gauge stays on full then the fuel gauge sending unit needs replaced. If the gauge goes to EMPTY then check the circuitry on the back of the instrument cluster as well as the pink wire from the sending unit. If circuitry and wire is OK then this also points out a faulty fuel gauge sending unit.

When the gauge was stuck on half full I replaced the sending unit and the gauge went over to the fulll mark. But it still remains on full even with the ignition off.

Have you drove it anywhere to use some gas? If it reads fine with ign. On then wouldn't worry about it. If its stuck on full then there is still an issue and if the sending unit was already replaced it must be something with the instrument cluster itself or wiring.