Not sure what had changed in the W210 vs. the W124 in terms of seat mechanics, but I concur, that the headrest drive pinion is broken.

The headrest drive components were under $20 when I got mine.

As Lenny Lipscomb stated, access is gained by removing the seatback cover.

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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