It would be nice if I could keep it running with zero villagers . . . most games, being an avid modder, I can just crack open the files for answers like this, but here, alas, it seems only the visuals are accessible.

The problem is, it's not possible to calculate exactly; I expect there's a random element in how frequently they eat, and without sitting there constantly clicking on a tree, it's not really possible to monitor that. I don't think it's possible to keep a log of what time it changes, but I'll see what I can find out.

EDIT: I can at least say with assurance that it does not occur once per hour, at normal speed.