Watching the video, it appears that it moves when there is a lot of foot traffic. It doesn't seem to move at night. Without seeing the statue first hand and being unable to examine the case., I suggest that the base of the statue has deteriorated over the years and has made the base slightly off balance/center. People walking by shakes the case slightly and the statue turns minutely. Enough vibration during the day would turn the statue around.
Just my thoughts.
Yep, I take the fun out of everything.