I know this is weird but when I’m backing up in reverse and mash my brake it feels like something is moving underneath. This doesn’t happen when going forward just reverse.
When you say it feels like something moving, what do you mean? Like a knock/clunk? I'd start with checking all your control arm bushings. Also, pull the rear drums and make sure the hold downs for the shoes didn't break.
It’s not really a clunk just feels like slight movement. Almost like when you pull a trailer and you brake and feel the movement on the ball. That’s the best way I can describe it. Only in reverse though.
Stick a prybar between your belly plate and your transmission mount. Gently pry up to see if your mount has deteriorated, and the cause of the movement you feel. Check your control arm bushings for any movement, shocks, trackbar, etc. Good luck
What year TJ? Is it 03/04+? If so, those year had something i recall reading on the caliper where the first braking in reverse after it sits for a while feels like a chatter almost. Nothing to worry about, my 05 LJ does it too, only for the first time I reverse brake after that its find. It's something to do with the pad seating themselves on the guides on the caliper