Did you test it on the bench in the same orientation as when it's installed? As the bearings go bad, the brushes loose contact with the armature/rotating part of the motor. Setting the motor on it's side or even moving it may allow temporary contact. Did you test for power at the motor wires?

Blower control is effected by directing voltage through a number of resistors to reduce blower to a certain level. Full voltage goes to the blower for max blower setting, voltage through 4 or 5 resistors goes to the blower for min blower setting. The push-button unit sends a specific signal for max, min and DEF settings, and a modulated signal as determined by the temp control unit for the AUTO setting.

I had an early W126 ACC unit that would only engage the blower motor at max setting, and another early W126 ACC unit that would only start the blower motor at max setting. In the second car, I could swtich to AUTO after a minute of having the blower at max setting. Never figured it out. Maybe things you can check.

Sixto
95 S420
87 300SDL