ok so I had this issue before on my 86 sami. I have a auto ez locker in the rear. I noticed a while back the output shaft for the rear diff was loose. I was told to just tighten the lug down. That worked for a while. Now i have a loud popping everytime i turn tight because the locker isnt releasing when it should. I looked at the the lug where the shaft meets the differential and it was loose. So i tightened it up again but it will still wiggle around.

The nut seen in the picture is the pinion nut and is actually the INPUT to the differential.

It's also not as easy as just tightening it down - that nut, along with the crush tube inside the differential sets the pinion preload, and those two together with some shims set the pinion position which is critical to the life of the differential - it's also normally staked to prevent it from coming loose.

You possibly have a collapsed bearing in the differential - especially it it still "wiggles".

Sounds to me like the third needs to be removed and replaced, or rebuilt.  I would guess the pinion bearings (the pinion is what that nut screws onto) are shot.