Well, that didn't pan out, unfortunately. Engine speed doesn't seem to matter. Now happens regardless of shifter position.
The only constant is that it so far only happens when the brake is applied. I am still suspicious that that's a major clue. My brake/shifter interlock hasn't worked for a couple of years (i.e., it lets me shift out of park even if the brake is not applied) which makes me doubly suspicious there's some connection.
I took the wood cover off the center console to look around. The two grounding points look good and tight. No obvious shorts anywhere.
I would love to know how the shifter/brake interlock system works. I've looked in the MB CD ROMs and in my Haynes manual and I can't find any reference to this system. Anyone know how it works, and if there is some way for these two symptoms to be related?