[David Fulford]

Your 66 came with either an 8" or a 9" rear end. 8.8s came way later. If it's on 8" rear you would be able to get a socket on the bottom most bolts that hold the third member in. If it's a 9" rear, the way it is maid only allows access to those two bolts with an open end wrench. You can also get information from the driver's side door tag and that should tell you numerous things such as whether it's a trac lock etc. One way to tell that is to jack the rear of the car up and support on jack stands. Turn one of the wheels forward manually. If the other turns forward, it's trac lock.
If it turns backward, it is open. The rear end could be an 8.8 but most people transplant a 9" into a classic stang instead of an 8.8
And on the rear end, it sounds as if the gears we're not set up correctly and are making noise. If they are not to worn already, you could pull the third member out and have the lash reset on them by a mechanic. Although it's probably better to just replace the ring and pinion.