Since creating that post, bouncing ideas with some other users has lead to solidifying my belief in this new updated description.
Rob562 at wdwmagic noted the top edge of the mirror's frame lines up with the chair rail on the wall and suggested the lower wall is the only portion that moves. I had discounted this previously because that would requires the horizontal movement of the mirror does not exceed the width of the mirror frame to avoid gaps or seeing the moving wall behind the mirror. But looking at the videos again, the horizontal movement does appear to be less than the width of the frame, and this simplifies operation significantly. I'm convinced this is the correct description.
For the mirror surface itself, the consensus is that there is a solid mirror at the start and the segment of the animation where the wood doors slide in from the side is designed to conceal sliding the mirrors to the side to make the opening appear. Supporting this is that the animation is the full length of the mirror, the place where the doors meet is black, and the speed of the animation moving across the mirror. This allows a solid panel to be used in the start position, then later slide to the side with a matching panel following it, and at the finale, the two panels slide open to reveal the doorway.
This new animation illustrates the simplified design. A single panel at the bottom, with the wall area directly behind the mirror frame sides being empty at the start position. The wall and mirror in this diagram are semi-transparent to allow seeing the moving elements behind them. The mirror frame extends side to side, and still extends vertically with the bottom wall panel. The seams of the wall panel are obscured by the chair rail, the vertical columns, and the props in the room which sit at the foot of the mirror on the floor.
Here is the new animation
There you have it. The location of the projector that shows the mirror images is still a mystery to me, but I believe it to be behind the mirror possibly up high in the ceiling so it is out of view when the mirror actually opens.
Share your thoughts!