I doubt that this would have to do with grounding of the cluster, and IMO, it would be easier just to pull the sender out of the tank and figure out what's wrong with it than to try to defeat the indicator light.
On second thought, it might be whatever relay whose job it is to light that light up when you first turn the key (to check that it works) might have stuck open- or did they start doing that on the '83s.
