Something loose in the suspension, like control arms or tension struts. Braking will typically set it off, ie initiate the vibration.

There is nothing to release the caliper except the rotor runout pushing the pad back in. If it was seized, it would stay seized.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue