Mine has done this religiously upon startup since I purchased the car 6 years ago. Never gotten worse either.

I never got a consistent answer from anyone on the source of the buzzing...so I lived with it and chalked it up to a "personality" trait of the W124...

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2009 ML350 (106K) - Family vehicle
2001 CLK430 Cabriolet (80K) - Wife's car
2005 BMW 645CI (138K) - My daily driver
2016 Mustang (32K) - Daughter's car