Sending unit or the float is starting to fail. It's part of the fuel pump assembly, and to change requires dropping the tank. You can either live with it until the pump itself fails and change the assembly out or drop the tank and swap out the sending unit.
It could also be the actual gauge panel in the dash, itself. Chevy had a recall on gauges. Often times Gas gauge & Temperature gauge would go out and sometimes just plain stop working. If you haven't fixed it yet go to www.AirBags.com. They fix air bags but also OEM Warranty for life, repair/replacement of dash gauge panel including bulbs & power supply. Way cheaper than dealers from $300 to $600. This place charged $75 for repairs, $33 to ship back- $108. You pay $24.00 to ship to them. Get back in 24-48 hrs. with a life time warranty. They are in Duluth, Georgia. I used them. Great pricing, fast shipping and so far, mine has worked for 3 years.
Another reason I knew it was the gauge panel is that first the Temperature gauge started not working right; radiator wasn't overheating etc. Then the Gas gauge. So I had to remember how much gas I put in (assuming I was getting 20 mpg) so I didn't run out. Gauge wasn't accurate. Got gauge panel fixed.
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