Very often. I can't tell you every XX minutes, but if that effect is in working order, you wouldn't have to stand there but a few minutes to see her, seeing you!
Yes, that would be my guess as well. It is often, but only people close to the door can see it clearly and I don't think it is anymore than that between eye opening. There are a lot of people that don't know it even happens so they aren't looking for it. It happens really quickly.
It might help those reading along to note that this thread is discussing the Madame Leota burial tombstone/monument that sits in the graveyard just outside the main entry doors to the Haunted Mansion.
(To the guests' left side, as they face the doors.)
The tombstone appears to be made of carved granite and features a bronze-tone facial likeness relief of Leota that is facing toward guests who are waiting in the very last section of queue before the doors open into the foyer of the Haunted Mansion.