Rear end question?

If the wheels won't turn independently of each other, then it's most likely that you have a Limited-Slip differential, if it's original to the '67. --(Ford Traction-Lok differential didn't come out until 1969).

It's also possible that some previous owner could have installed the differential. If that's the case, then there's no telling what it actually is short of pulling the 3rd member and looking at it.

A quick way to tell if you have an 8- or a 9-inch is to get a 9/16" socket and a 9/16" boxed-end wrench. There are (10) nuts holding the 3rd member to the rear end housing. If the socket will not go onto either of the (2) bottom nuts, it's a 9-inch. (only an open-end wrech will easily go on them). If the socket easily slips on, it's an 8-inch.

Did the tires spin in the same direction? Then use you have limited slip diff of some sort
Did the tires spin in opposite directions? Then no you do not have a limited slip of any sort