I have a 97 SSEi and have fuel gauge problems as well. My problem is that the gauge never goes below 1/2 a tank. Sometimes when I first start the car, it will show correctly then slowly work it'* way back to full. Most of the time it shows somewhere between full and 3/4 of a tank. I assume the sending unit is bad. Just haven't had the time to replace it.
Let me know if the resistor fix helps your problem.

I have a 1997 Riviera with this same EXACT problem! Except mine works fine until I get down to 1/4 of a tank or lower, then it will slowly go back to full. It drives me crazy! Once I get lower on gas I never really know how much gas I have. I hope it'* not the sending unit, those are like $200 I've heard. :(

My gas guage is getting flakier and flakier. I used to be able to trust the low fuel light but not the guage. I ran out of gas and now I don't trust the low fuel light.
I'm going to try the service bulletin repair in this thread.
It'* ok to do it on a '96 isn't it?

You know, I don't think that the repair described in the TSB would work for you. You may have a different problem with the sending unit or the instrument panel. Did you ever use Shell gas regularly?

We don't have any Shell stations in the area. I doubt if the car has ever been to a Shell station. The gauge has always been like this, but lately it'* gotten worse.
It acts like 1595beekers' acts.

fuddyduddy, I know this is an old thread, but I noticed that you mentioned using Shell gas. I recently used shell gas and my guage is flippin' out on me. When it'* full it will zing back to empty and continue to do that. Is it a Shell gas problem?

Shell had an additive in their gasoline that would gum up the fuel sending units and cause the gauge to be inaccurate.

the gauges are wacky. when i fill my tank the gague will stay above the fill line for about 150 miles, then drop like a rock after that.

That'* "normal" behavior for a 92-99 Bonneville.

dude...i had the EXACT same prob w/ my 92 ssei....it would **** me off...stupid thing..anyways my boost guage was off and my other guage dont rmeember which wa smessed up too...got a whole new instrument cluster htingy...bout 250 bucks...