It's both. Pressing against the trunk release button with your finger kills almost 80% of the rattle. The rest seems to emnate from the rear decklid (I have seen some cheap fixes for this, so I'll try it).
Boots, how do you tighten that latch?
It puzzles me knowing that I have seen other E36s with systems more powerful than mine with no sound deadening either, yet they have far, FAR less rattle than my car