Taking a complete flier: That
sounds like an textbook issue with grounding. From looking at the circuit diagram, it appears that power to run the various lights and this gauge comes in on a yellow wire, and the gauge itself is simply driven by resistance via the brown wire that runs back to the tank sender vs resistance at the gauge panel itself...the tank sender has a variable resistance, and (for want of a better explanation) "the harder it grounds the further the needle swings." So there's no magic there - it'll either work or it won't. Page 10-77
here.
From looking at the wiring diagram, page 10-100
here, there's supposed to be a gauge cluster ground (maybe shared with the cigar lighter?) tied apparently somewhere on the side of the brake pedal support. Is that present? I can't tell for sure, but it looks like the ground should "come in" on the round connector on the instrument panel - terminal E. Not sure if there are other ground connections.
Regardless, if the ground isn't present (or the ground isn't fed through to the instrument panel, or there's a broken trace on the panel) then the gas gauge won't ground "properly". It'll still
try to work, probably grounding through whatever paths are available (like via the turn signal bulbs?), and I'd expect all sorts of weird things to happen. Like...with the car just sitting there, key on engine off so the oil pressure light is on...does using the turn signal cause the oil pressure light to flicker? Does pulling the turn signal indicator bulb cause the oil pressure light to dim/go out? If so, that really does sound like a grounding issue.
Not sure if you can get to the instrument panel in-situ to test the ground, but if you could measure resistance between the instrument light grounds and the chassis (or heck, the ground lug on the fuel gauge vs chassis), anything more than a few ohms of resistance would spell trouble for your gauge.
