Fuel level sensor. Its not even a sensor, its just an piece of plastic with some fingers on it that run across a circut board and that sends the info the computer. The fingers wear off and cause the wacky gas gauge.
Search the problem on here and you'll find tons of info. Also search on youtube "bonneville fuel level sensor replacement" and watch the vids.
I second this. I had a very similar problem and the dealer told me to replace the entire pump and sender unit. I said no thank you and tried what that guy did on the video. I was amazed at how easy it was, just buy the exact piece and follow the video, it wasn't difficult and took me less than an hour. It has been working for about 4 years now. Best of luck.