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It's not just a problem in vettes. I've got a 99 GMC 4X4 pickup that's been doing it for over two years. Local garage says they've seen a ton of GM's that do the same thing. It's the sending unit alright, gets gummed up by the sulfur content in the gas. I let mine go for a long time and have been using Techron additive for three months now with every fillup and it seems to help it somewhat. The problem's always worse when the tank is newly filled and the sensor is immersed and then improves as the tank falls below 3/4.
Try the fuel additives. Redline, Chevron Techron or some others have been successful at fixing this problem. And start using Chevron or Amoco gasolines.
If that doesn't work you will need to replace the sending units. There are two of them. I had both replaced before my gauge was fixed. It turned out to be the left side which is more of a pain to replace (from what I was told).
Had the sender replaced in my Wrangler at 20K for the exact same problem; if I had not had a five gallon can of fuel attached to the rear bumper, I might still be in a desert in Utah. On the trip home, it would rear half, then full, then one-quarter, up and down; drove home using the trip odo.