i believe it could also be a grounding issue. i seem to remember I had the same issue wit my cutlass

Well, I'm willing to bet you have a P0463 Fuel Sender circuit high, Stored in the computer, it won't turn the light on, but you need a fuel sending unit. the "fingers" on the rheostat break off and the circuit goes open, then the gauge drops to empty then to full, but sometimes reads normal. Real common problem with GM vehicles from 98-06