I bought a 2001 Silverado 2 weeks ago and my truck has the same issue.
Seems as though when I top off the fuel gauge needle fluctuates less but when @ 1/2- 3/4 tank the gauge needle flucuates anywhere's between 1/4-3/4 a tank of gas while driving. Also, when parked and idling or if at a long red light the fuel gauge needle drops to empty and then the orange fuel light glows and stays on but as soon as I move the gear selector to drive the fuel gauge needle moves to about 1/2 a tank and the orange fuel light goes off .
Had me freaked out until after reading about the issue.
I pretty much keep track of my miles driven and gallons purchased until I can have it fixed.