I agree, it's a commom problem. The rear differential mount has gone. It's probably old as your car and needs to be replaced. It's made out of rubber. It's not that hard to replace. United Z Club L.A./LB. Sy.
Mine is doing the same thing. I think mine is the mustache bushings. I read somewhere that you can slide a floor jack under the diff. and jack it up. If the diff moves at all before the car does it is definately the mount. Don't know if that's a true test or not.
I also had a clunk from what I thought was the rear between shifts, but AL260Z suggested the ujoints on the driveshaft....I thought NOOOOOOOOOO, it's coming from the rear. Well, it wasn't...check the ujoints....that's all it was with mine. 78Z
One thing you might check on the "Clunk" which helped me isolate my problem on the 71. That is does it clunk when backing up and does it clunk when starting out. My clunk was a badly worn U joint on the right half shaft. Good luck!!