Low fuel light comes on and stays on but tank is full.

You can remove the negative (black) battery cable and re-set your service engine light or got to your local auto parts store and they can re-set your codes with their code-reader - as far as rough running, maybe some debris was allowed into your fuel tank and needs to be dissolved with a fuel system cleaner like Chevron Techron

fuel sending unit inthe tank acting up thse models have susceptical of sulfar from gas building up on the unit u can try chevron with techron fuel cleaner in the tank wait a few days see if that help if not not u need new fuel sending unit

I had the same problem with my 98 Corvette with 69K miles. Mine did exactly as you described soon after I purchased it in November of this year. I went online and read posts of others with the same problem and how to try and fix it. At 1/4 tank add 2 bottles of Chevron Techron cleaner and fill up with good name brand premium fuel. The Techron cleaner will clean the sulfur residue and other contaminants off of the fuel level senors in each of the left and right hand side gas tanks (C-5's have two gas tanks on either side connected by a transfer pump with each side having it's own fuel level sensor). I did this and so far after nearly 3 tankfuls there's been no recurrence of the problem. However, if this doesn't help then the alternative is to replace some if not all of the components mentioned earlier. I got a $1300+ repair quote from my favorite garage prior to applying the above fix. I'm no mechanic and I may have some of the actual part names incorrect. I hope this helps you out and fixes your problem! BTW, you can also use a full can of SeaFoam cleaner in lieu of the Chevron Techron cleaner. I used the two bottles of Chevron Techron the first tankful and used SeaFoam in the second tankful. I plan to use a bottle of SeaFoam every 3-5K miles to help keep this problem at bay and keep my fuel system cleaner!

you may need a new fuel level sensor. sometimes the sensor gets a coating on it from the fuel and you can put in Chevron Techron, fuel system cleaner, to clean it, sometimes that will get it working again. If not, then it will need replacement.

The fuel gauge sending unit which sends a signal to the gauge is stuck or defective. It’s in the fuel tank.

Buy 2 containers of Chevron Techron at Wal-Mart and add to the fuel tank. Sulfur deposits build up on the sending unit. I own a Corvette and many of us owners have had to add the Techron to cure the fuel gauge problem.

If that doesn’t take care of it, more than likely the fuel level sending unit has gone bad, it is inside the tank and is a variable resistor connected to a float. Chevy and GMC trucks in the 99-2003 era have had a bad problem with this. The sending unit can be replaced apart from the pump but this is not a job for a beginner.

It’s best to replace pump and sending unit at the same time. If you only replace sending unit, pump will usually fail soon after that creating extra expense

clean the MAF sensor first and also add some Chevron Techron fuel injector cleaner to 1/4 tank of gas. You may have a dirty MAF or a partially plugged injector.

Just go buy some fuel stabilizer and top off the tank and drive. Two years isnt that bad. Then on the next tank use some injector cleaner. I like chevron techron fuel injector cleaner added to a full tank of prem 91. This is just a prevenitve measure to clean any varnish that may accumulated on the injector nozzles.
Then use 87 octane if thats what you normally use.

it could be plug wire, the spark plug, or the fuel injector.
If injector, try Chevron Techron Fuel tank additive first. Add one bottle to 1/4 tank so it will be more concentrated.

It sounds like you have a fuel level sensor problem. The fuel level sensor attaches to the fuel pump inside the gas tank. The tank will have to be removed for access. The fuel pump assembly comes out of the top of the tank,and the sensor can be then be replaced. Removing the fuel tank is the major expense. The sensor runs around $120.00.