I don’t think the sending unit is the ground, there should be a ground wire that runs from the sending unit to the frame. The tank just sitting in the saddles would be a terrible body ground. It actually sites on rubber or tar paper in there from the factory to prevent squeaks.
If it is bouncing from full to zero constantly, sounds like a ground wire problem. You could try to run a ground wire from the frame to one of the flaps of pressed welded tin on the tank with a self-tapper and see if it fixes it. Of course if there is a lot of corrosion around the sending unit where it meets the tank, this won’t work, but it’s easier than pulling the bed off as a first step and the sending unit is under the cab anyway, not the bed so the way to do it is drop the tank.