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I think fluctuating is normally caused by a loose connection between the feul gauge and the sending unit on the tank. (normally the sending unit) I would guess an 82 holds about 15 gal, owners manual should say....
Owners manual says 23.7 gallons, but when I filled it up the first time it only took about 12 gallons and it showed between 1/4 and empty (I think)....
You probably need a new sending unit for the gas tank. My thirty year old just had it's sending unit replaced. The symptoms were exactly the same as yours and once the new unit was installed....everything is back to normal. Mine actually went above the F by 1/4" when filled up then worked pretty well until around a half tank. Then...it bounced around all over the place and I really didn't know how much fuel I had. A mechanic can test the sending unit without removing it, so you should be able to make the decision easily.
jwatty, inside the tank there is a flat metal strip that goes from the sending unit up to the insulated contact that goes through the tank access panel and the wire to the guage attaches to this pin. That flat strip has a plastic cover and that cover cracks or seperates from the metal strip and allows it to touch the tank grounding the sending unit. also that pin through the access panel can sometimes lose it's insulation and ground the unit. I've tried to fix mine twice , but it only works right for a little while. I guess I'm going to replace my unit. Hershey :chevy
The sending unit is in the gas tank and the gas tank has to be removed to get to it. At least that's the way my '69 is......
The good news is ...the sending unit for a '69 costs way less than some of the newer models.