I'd say it's the sending unit. I'm not sure where it is located on the F150. I had one go out on my '88 Ranger and I had to drop the tank to replace it. If yours is in there too it would be a good opportunity to replace the fuel pump and in-tank filter as well. It's only a matter of time before they go too.
I hear this is a common problem with these trucks. Fuel level sending unit. Both my tanks always read F until about 1/4 tank and then go wacky until they are almost empty then read E. At least with 2 tanks I always have a reserve.