1999 Pontiac Grand Prix _ I wish it were true, but

fuel gauge periodically reads full when the tank is not full

That means your fuel sender is failing. It is in the tank and I think, part of the fuel pump assembly. You might try a bottle of Techron (read the instructions) in with the fuel to clean it off. Given the car’s age, and possible mileage (100K +) it might make sense to change the fuel pump before it fails and get 2 birds with one stone.