Why does the gas gauge move while sitting still on 2002 Chevy Silverado 1500?

Crummy fuel guage sending units. The GM trucks are notorious for that kind of thing. Solid vehicle mechanically otherwise though. The above answer is correct but to maybe help a little more, try adding some Techron to your gas tank. You can buy it at Walmart or Pep Boys or AZ. Some of todays fuels have a lot of sulpher content and this adhere's itself to the fuel sending unit. The Techron helps dissolve this. I own a 2004 Corvette and a lot of Vette owners were advised to try this to alleviate the fuel sending unti problem and it worked for a lot of us, NOT ALL but it may help. Then do a google search for TOP TIER GASOLINES or TOP TIER FUELS> There is a list of gasolines that have the right additives to help with this problem. I buy Conoco or Chevron or Texaco which already have the Techron additive in it so I don't need to buy it separately.