However, the design of output stage to the motor will affect this voltage or effect behaviour. Is there a half bridge or is there a single transistor where a protection diode is placed in parallell to the motor?
Assuming the fan motor is inductive and the output stage is a half bridge. Then the dc voltage (as seen from the motor) should be around half as much. If that isn't enough (motor isn't pure inductive), the half bridge can be followed by an inductor to make a (almost) steady dv voltage and there could be a cap parallell to the motor. That should give output ≈ 6V.