FWIW, the transfer case motor probably won't move at all when selecting "Auto" from "2WD" mode, since the PCM will only operate the motor IF tracton loss is detected, then drop it right back out following a time delay. I have two Astros with full-time auto AWD, and that's how they function. My daughter has an '06 Envoy V8, and that's how it operates in AWD mode.
You will probably have to select 4WD (High or Low) mode and then either 2WD or Auto to force the case motor to move. The transfer case motor can be very quiet. You may have to listen from under the vehicle while someone actuates the controls to shift the ranges.