Ok, I think I have it. As the beam sweeps around and hits the VOR antenna. if the receiver detects that the OBS setting and the beam heading are the same, it activates the "From" indicator. If it detects a 180 degree difference, it activates the "To" indicator. I understand that there's a little more to it to get the "To"-"From" indicators to handle the whole half-circle of headings, but now I see the basic mechanism.
It's all a pretty brilliant system given it's age and that it could be implemented with a box of vacuum tubes.
Thanks.