I am afraid that I cannot offer help but can confirm that I have had the same problem and it appeared to be an easy fix. I had exactly the same symptoms on a W124 300D way back in about 1992. I was on holiday in France at the time and took it into the local dealer on a Saturday morning. Their mechanic drove the car, heard the sound, took it round the back and returned it about half an hour later, fixed. I have no idea what he did to it. There was no charge. So perhaps there is some hope here!

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