That's that thar GM trick fuel guage. lol.
Mine does that although the 02 does not have the low fuel light.
The culprit is the anti slosh module. It's job is to slow the movement of the needle it does this by delaying/smoothing the voltage from the sender. Without it the gauge would constantly be moving as the fuel in the tank moves.
When you cycle the key, the tank sender is read and that is where the gauge starts.
