[Hozer 88GTConv]

I just replaced my sending unit after having the same problems you described.
It turns out, the worst part was the two-wire connector on top of the sending unit had completely corroded and that's why the signal would vary from full to empty, because of the intermittent ground.
If you have access to a junkyard, I would consider just getting the grey plastic connector housing and a little of the wire and just tie it into you existing wiring.
Obviously, you have to drop the tank but it is only two 15mm bolts holding the retainer straps. The sending unit housing is the one in the middle center.
and it goes w/o saying, make sure you get as much gas out of the car as possible. A mustang tank holds 15.4 gallons and it can be awkward to handle even with a little fuel in it.
If you need a new unit or wiring, http://www.50resto.com has 'em.
Good luck.
no smoking either, but drinking is encouraged.