tl;dr: the most recent villager is supposed not to be able to move out according to the game code, but some people have reported it happening to them, so it is possible, just extremely unlikely.
I wanted to move Genji out so I could move in Punchy. To do so, I tried the time-travel/thought bubble method. It had been at least three hours and Genji hadn’t had a thought bubble once—and he was my latest to move in.
I would say if you want to force your latest villager out, it will be much, much harder.
I don't think it's true, as I recall having a villager who has only lived in my island for a total of four days. As others have stated, it's completely random, but I have read elsewhere that there are methods to shift the move away bubble to someone else by exiting the game. I haven't read up about it too much, since I usually just let it happen naturally.