What would cause the RPM to fluctuate between 350 and 600 when in Drive or Reverse and your foot is off the brake pedal with the car moving under idle?

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2006 BMW M5 "Heidi" @ 109,000 miles
2005 MBZ C55 AMG "Lorelai" @ 165,000 miles
1991 MBZ 300E "Benzachino II" @ 165,000 miles
1990 MBZ 500SL "Shoshanna" @ 118,000 miles

(On the hunt for a good used M103 engine as of 6/10/23, PM me if you have one to sell!)