Kyle,

I think it is what "can-do" touched on earlier in this thread, what he called "the driveshaft support rubber as well it's mounting bolts"

which is what I would call the "Center Carrier Bearing".

If you take a good long look at the this thing, (located at the break point of drive line) you will see what it is suppose to do.
Without good strong rubber surrounding the bearing itself, but instead weaken and frail rubber, maybe this mystery noise could be the result when peroids of power transfer back and forth between transmission and rear of car.
When you think about it, the engineers could have easily designed the bearing without the surrounding rubber. It must serve a purpose.
I have a 240d 4 speed as well. I know on my car I can move/push the drive-line an inch in either direction, I feel after 20 years the rubber may be tired.
I may replace mine, (depending on cost of part) in 03, as sort of a routine maintenance (you know, every 20 years whether it needs it or not) sort of thing.
By the way, I did have a Center Carrier bearing go bad, once in a Datsun truck and to my best recollection there was a lot of thumping going on.
good luck