Welcome to Just answer,
The most likely cause and is a common failure is the sending unit inside the fuel tank.
Your in luck!, On your car you do not have to remove the fuel tank for access, in the trunk there is a cover that gives access to the fuel tank sender.
Relieve the fuel pressure by removing the fuel pump relay under the hood and starting engine an let run out of fuel.
To get to the cover open the trunk and remove the floor covering, you want to make sure no carpet is left in the trunk because spillage of gasoline is a real threat and the car will smell like gasoline for weeks. Next remove the seven bolts holding the cover, then remove the cover. Next the fuel lines and wiring connectors are removed then the snap ring that holds the module down is removed, and then the fuel pump module is lifted out of the car, there will be gasoline inside so keep upright!.
The fuel level sensor is on the side of the fuel pump module and is a resitor card that the contacts wear and causes problems such as the one you are having.
Here are a few diagrams that support the text above. If you have more questions please reply back.
Rear trunk trim and carpeting.
Fuel sending unit Level sensor
No problem I trust that that you will accept when you are satisfied with the answer,
The one that is labeled fuel level sensor (the last one).
I checked with NAPA online and it does not show the part available, but a phone call to them would not hurt, you will be asking for a fuel level sensor. If they don't have it ask them if you have a local parts store that handles AC delco parts and then request thier phone number. If none of these work, you will need to contact a local GM dealer.
No, there are no extra charges, you can always reply back.
Let me know if there is anything else I can do for you, or if you have more questions.
I apologize, I misunderstood,
Part 5 in the diagram is the fuel level sensor. It has an arm with a float attached that floats on the top of the gasoline, on the other end is the resistor card which fails. There will also be a wiring harness attached to the replacement part.
How did you make out finding the part?