Just started doing this noise. When I get to a light I apply the brake and the Jeep stops fine, but then I hear rattling from under the shifter area. I let my foot off the brake and it thumps and moves the jeep even before I hit the gas it thumps. Like a bowling ball is loose in the back. The bolts holding the diff look tight. Bushings look good. And the drive shaft dont move when I shake it. What else do I look for?

 

Your drive shaft doesnt move at all? I had that problem and it was my rear pinion yoke. My drive shaft mover side to side. I would look at u joints. Are you lifted at all?

 

Put the e brake on then put it I neutral and you should find that your u joint is bad. If not jack up the rear put it in neutral and check the yoke along with the entire 3ed member. I guess u joint. The rattle try lifting up your 4x lever when it is doing it at a stop. Just a little your linkage probably needs to be adjusted. Not a big deal and not related to the thump.

 

My jeep has no lift it's stock. Will try the e brake thing to see if it moves.