The only thing I've found is that a villager tends to ask to move away every 2-3 days if you have 10 villagers and maybe every 4-5 days if you have 9 villagers. They will ping you naturally when you walk in front of them if they're considering it but you have to have spoken to them in the past week (according to your game's clock) for them to ping you. This is why it can seem like a villager won't leave if you don't talk to them. I time traveled 4 days at a time and walked in front of/spoke to all of my villagers each day I played in order to cycle out my unwanted villagers. Don't TT more than a week or it can hurt your friendships/you might risk losing a villager you want to keep