My new Carbon Footprint from Government Motors came to me with an inoperable fuel gauge. It had 2 modes, 125% full and -25% empty. A quick search of the topic revealed some 2.3MM hits in no time at all so this must be fairly common. The no-brain fix is to replace the whole fuel pump module which runs $55-$555/ea depending on the source. NAPA quoted me $315-$350.
Alternatively you can get a small piece of sheet metal that snaps onto your sensor arm on the fuel pump for $23 + shipping.
Summit Racing Equipment and that fuzzy rectangle in the round white spot on the lower left is it.
On my car the fuel pump is under a cover plate, under the carpet in the "trunk" area. Your location will be different. Installation is not hard, it took me about an hour and it seems to work. Mine has been in about an hour with no drive time on it but if it goes south on me, I'll mention it. A $30 fix.