Does your shifter have any slop?
I'm guessing that your reverse lights still work, it's just the slop in the shifter not allowing contact with the switch. Your SL has 200K on it and I bet it needs a set of shifter bushings.
Try moving the shifter a little, while braking in reverse, somewhere where you can see (or an assistant can tell you) if the reverse lights come on.
'73 280SEL 4.5 (9/72)- RIP
Only 8,173 units built from 5/71 thru 11/72
'02 CLK320 Cabriolet - wifey's mid-life crisis
2012 VW Jetta Sportwagon TDI...at least its a diesel
Non illegitemae carborundum.