So, the relay I ordered arrived today...only it wasn't the one i ordered. While it looked very similar, it only had four active pins. It also didn't have the clear fuse door that mine had. Looking at the number on the side answered why.
The original relay had "89 71 34" stamped on the housing (Mercedes part#2015400845). The new arrival had "89 71 24" stamped on its housing (Mercedes part#1265404745). A little research came up with the fact that this relay was meant for a W126 among others, but not a W124.
All was not completely lost, though. The diagram indicates that the circuitry in each is identical with the exception of one missing output.
So, I decided "what the heck" and installed it in the car. Upon firing up the engine, the tach began to work, and the idle was back to normal. The missing output apparently is for the ABS as the warm glow of the ABS warning light continued to brighten my day. I might have been able to get the same information from the manual, but I'm not so sure since both output pins are marked "87". I didn't look, though.
I have contacted the seller to (hopefully) get it exchanged to the proper one. Meanwhile, I hope this info is useful to someone.
Cheers!