That is a common fault (there's also one on the rear suspension, obviously) but the arm being knocked off will not stop the headlights from cycling up and down at switch on. Halogen cars do this too to exercise the motors.
There is a fuse for the headlamp motors: if they're not moving at all that would be the first thing to check.
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Ian
Current: 2021 G21 330i M-Sport
Previous: 2018 A6 Avant S-Line MMI+, 2014 F31 320d M-Sport, 2013 F10 520d M-Sport, 2011 F10 530d M-Sport, 2008 320i M-Sport Coupe, 2002 325i, 2001 318i valvetronic, 1998 318i, 1996 525i, 1990 Porsche 944S2
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