1994 yj stretched, locked and loaded - 6.0l vortec lq4, 4l60e, np231, Dana 44s 37" interco trxus m/t, 3.5" bds front leafs, double triangulated 4 link rear on xj front coils.
1997 ZJ limited - BONE stock
2003 tj - 4in skyjacker, 33" mickey thompsons
my on board alternator/welder write up
my tj 1/2 doors on a yj write up
RC vs BDS
Finally got around to checking the rear out and this was all that I found. The 2 body mounts under the passenger door have slipped or the bottom rubber mount released. Not sure if this is whats causing it but everything is just fine. U joints, U bolts, springs, brake drums, hubs, wheel nuts, exhaust doesn't bang into anything, gas tank cover isn't loose, shocks and shock mounts are fine. I did however find that the rubber suspension blocks/bumpers are missing on both sides.
I had the exact same scenario. For me it was the track bar. I replaced the bushings and it went away. However Since then I've yanked em both and they now collect dust under my bench. Your body mount doesn't look so hot, it could be possible that's the culprit.
Mine did the same thing when the Jeep flexed a little, like leaving the driveway and such. Turns out that one of the body mounts for the rear leaf spring was wallowed out, allowing the spring bolt, hence the spring eye, to shift up and down. I've been meaning to weld some washers or something in there to make it round again, but never got around to it. Right now it's just extra tight which helped.