Does the faulty sender have a brass float or a nylon one? I'm thinking that it could have a hole that's allowing it to fill with petrol, which means that it wouldn't then float, so no reading on your gauge.
That would be easy to solve, with a soldering iron. In the case of the nylon float, use the soldering iron to weld the hole closed, in the case of the brass one, then fill [the hole] with solder.
You'd need to place the float in some water and look for the bubbles as any hole in a new unit is unlikely to be visible to the naked eye.
No hole in the float? Then measure the resistance from one end of the winding to the other, if it shows that there's a break in the fine wire then there's your fault.
Lastly, check that the wiper hasn't fallen out of the end of the arm that carries it, this is a tiny (<3mm in diameter usually) carbon pin, they're only held in there by the wire itself.
You can repair the rheostat if the break is within around 2 turns of either end, then it would still read reasonably accurately. The wiper can be substituted by a chunk of carbon from a pencil, HB does the job.
Beyond those things, there's nothing to go wrong with a sender unit, they can always be fixed with patience and a little spot of fiddly work.
