My left wiper continued to run. I'm not really sure what my right wiper did; I think it was stuck in the upright position. Your problem sounds identical to mine. The fix is not horrendous. The part is $171 and you need to remove the headlamp to fit. In the meantime you can pull the connection to the headlamp washer pump so you can use your lights without losing all your washer fluid.

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JJ Rodger
2013 G350 Bluetec
1999 SL 500
1993 E300 diesel T
1990 190