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Sounds like an open or short circuit somewhere. I'll guess an open at the sender in the tank. (More resistance is actually a higher reading on the gauge at least on my '91) Do you have two tanks? If you do, does it do it on the other one? I seem to remember my gauges just stay where they were when I shut off the truck.
No, just the single tank. I am thinking of putting in the gauges with a tach so when I do that, if the reading dosn't change than I will investigate the sending unit.