Tiny metal “fingers” on the “wiper” portion of the float operated arm on the sender (fuel level sensor) get dissolved by sulfur in the gasoline. Then when the fingers move across a printed potentiometer on the sender, the signal becomes hit or miss… one, two, skip a few.
Sometimes they hit and send the proper signal and sometimes they miss and won’t write home.
I put in just the piece with the fingers in my Bonneville.
I was not supposed to be able to do that (Everybody says it needs an entire fuel pump module a$$embly), but I found a nice Youtube video. I had to buy a GM sender and use the part from it. It was cheap because GM was replacing them under warranty at the time.
The Bonneville was a cake walk to do in the driveway because the clever designers provided an access panel in the trunk through which I could withdraw the fuel pump module/level sensor. The part (sensor kit) was cheap, too.
Looks to me like a similar repair on that Saturn is going to require a tank removal, though. Then the person doing it will say to replace the whole fuel pump module! Sorry.