What could cause this? Bad relay guage float or what? Truck is a 1981 F-150

 

There is no relay that I know of in the gauge circuit.
Could be sender (float) in tank, Gauge, or any associated wiring. If you have dual tanks then the tank selector could also be a problem.

 

Find the wire that goes to the sender in the tank with the key on ground the wire [if your not near a termanal or a plug you can pierce with a sharp point tool if the gauge moves to full the problem is in the sender or float if not then the problem is in the gauge or wireing. Bubbabud