Looking at the wiring diagram for that vintage of PA-28 is instructive.
The power goes first to the left gauge, then via a jumper wire to the right gauge, so unless someone has moved the power wire to the right gauge and the jumper is loose or failing, that isn't likely the problem. But, the airplane is 55 years old, too, lots of time for stuff to get messed up.
The senders are simple rheostats, so unless the gauges read full when the master is turned off, which would be unusual indeed, their resistance will be at minimum when full, and at max when empty.
There were old cars that had fuel gauges that went to full when the ignition was turned off, but they did not use rheostats. They used a thermal device that made and broke connection in the sender, and there was a cam that flexed a bimetal strip that spent more time closed at empty than it did at full, driving the gauge down. The gauge itself was a thermal device, with a bimetal strip that curved when more current, or more frequent current, warmed it up. My '51 International pickup had this setup. Never seen it in any airplane. Cessna has used the rheostat affair for a very long time, ever since they abandoned direct-reading mechanical gauges in the wing roots. 1950s?
A shorted sender wire would drive the gauge to full.
The wire from the left gauge to the terminal strip is Q4A, and the wire from the strip to the sender is Q4B. The terminal strip connections look like this:
Q4A and Q4B are on terminals 3 and 4. There is probably a jumper bar across those two, and it might be loose or rotten or something.
What do I think is the real problem? Not looking at the wiring diagrams, and a reluctance to pull the interior out to get at the entire circuit. There is also the possibility of a loose sender wire at the back of the gauge, so has anyone been under the panel to have a look? The gauge itself might also be failing internally. It's old enough to retire.
Later 140s were wired like this at the terminal strip, perhaps to eliminate the jumper bar:
