Well, I time travel every 3-4 days, walk around town, and a villager will most likely ping you that they want to leave. You also might want to talk to villagers 'cause they might tell you if someone is thinking of leaving. You either say stay or leave when they ping you. If you want them to leave, but they change their minds, you just reset and skip to the day they were thinking of leaving. There are guides online if you get confused.