|one of the contributors if it is worn. The amount of movement in the video appears to be excessive but it would be helpful to know slack in a non clunk rear.
There can be other slack items like: the center main bearing and universal joints wear (if you have the OEM 2 piece DS), ring and pinion wear, differential output gears, worn differential support cushions (4 units), worn rear assembly to unibody support cushions (4 units), maybe others?
Next check with rear wheels on and clear of ground and car car supported safely on differential body grab either axel shaft and hold steady and rock wheel back and forth and listen to the outer axel joint. If noticeable clacking the joint is worn and a culprit to clutch engagement clunk.
Would be nice to know specifics of specific case fixes that were successful.