Today, I diagnosed my problem a little bit more precisely. It does not seem to be the sensor. With the mirror removed and both actuators travel full length back and forth. However, the tilt actuator makes some noise around the middle of the travel going in either direction. With the mirror on, the upward tilt can go all the way to the maximum height, but the downward tilt stops right when the clicking noise begins. For this position it can only be moved by hand.

I suspect it fails due to dust and worn lubrication/gears. Then, the electrical part detects a mechanical blockage of the tilt motion and sets a flag in the computer that no longer tries to adjust the position until the position is changed by an external force.

I could not take the motor assembly apart. I am probably looking at replacing it as a whole.