Check the other illuminated components throughout the cockpit as well...

...do the window and door switches, console switches and backlit climate control buttons flicker in the same manner?

I would still venture that the flasher relay has some trouble with ground.

In a related situation (on my W124), I had a ground problem with one of the terminals that housed a brake light bulb...whenever I depressed the brake pedal (at night), all of the illuminated cockpit functions would flicker rapidly!

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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