I'd think a day at a time, since the method of villagers moving out is a little different. They don't ping you if I recall, only walk around 'thinking' to themselves.
General consensus is at least 11 days at a time, personally I do 15 and it's a pretty foolproof method. Villagers will not move out unless they have talked to you beforehand so you are safe to TT forwards years at a time. I find that I get 1 moveout request every 12-16 days or so.
I usually time travel 1 month ahead, enter the game, then time travel another 5 days and usually find someone who wants to move. If I don't after the 5 day skip, I just do another 5 and it usually almost happens
I TT two weeks ahead and it works well for me. I TT another day if I don't see anyone out with the thought bubble and I find them most of the time after that.
I only do anywhere from 3 to 7 days once or twice and then I go back to my starting date and start skipping in that pattern again. This keeps me from going to far in the future and I have no issues getting the ping from my villagers wanting to move after a few times.