Sounds like the fuel level sending unit is toast.
It's mounted on the outside of the fuel pump assembly. I'll see if I can upload a pic for you. Of course it's inside the fuel tank so if that is indeed your issue then you can either drop the tank to access it or cut a hole in the floor under the carpet beneath the rear drivers side seat and access through there.
If your pump is running good you can replace just the fuel level sending unit. It's just a couple of wires and a plastic clip on the outside of the plastic pump body I believe. I've never actually replaced one without Doing the entire fuel pump assembly. If you go through all the trouble of dropping the fuel tank out of the truck then I would do the entire unit because that's a lot of hassle to go through twice.
Personally, my truck has an access hole cut in the floor. It saved me a ton of time. That being said, as often is the case with shortcuts, it can be dangerous because you are cutting steel next to a tank of fuel. If you're handy with an angle grinder it works like a charm but there's only a couple inches space between the tank and floor. Don't cut to deep or you might start a fire or explosion. I'm pretty sure theres a write up somewhere on this site about it.
