Many thanks folks, I did a magnified inspection of the board in bright light and found two suspect contacts. A careful resolder and the unit works fine.
The logic of replacing a suspect unit completely instead of fixing it is certainly valid, but there is surely something to be said for fixing the original and keeping it in the car to use as a spare when/if you again get a relay failure. It will save the $100 tow.
I'd love to know if you can safely swap these relays between cars. The one from the 190 will start the 300 and vice versa, but I wouldn't actually want to drive a car with a swapped part as perhaps it could damage a system. Any knowledge out there?

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'76 240D-Sold
'78 240D-Sold
'85 300 SD, 165K-Sold
'88 300 TE, 165K-Sold
'64 Porsche 356C Cabriolet- under restoration
'86 560SL 124K Miles-Sold
'94 320E Wagon, 74K Miles-128K Miles JUNKED
'06 E350 Wagon, 84K Miles
07 SL550, 14K Miles