The clunking could be any of the rear bushings, but in my case, I believe a similar behavior was the worn torque rod bushings. The t-rods keep the rear axel/diff from rotating. If they are shot the axel will be able to rotate a bit and clunk when the play in the bushing is taken up - stopping the rotation.
If this is the cause, then alternating braking and accelerating in either forward or reverse should cause the clunk each time you switch rotational forces on the axel.
Now I'm just guessing, but if your axel is in fact rotating back and forth, and if your u-joints are old/dry, then the rear u-joint might not like the increased angle of operation. This could cause the squeaking.
To diagnose, you might try putting the rear up on jackstands at the chassis jacking points and then spin the rear wheels by hand, raising and lowering the axel with a jack under the differential to simulate various weight transfer conditions.
Joe