Question: Does this actually make a villager move out?

[HopeForHyrule]

Ignoring them has never helped me. In one of my new towns, Boone was one of my starters and he was RIGHT in front of the town hall. I talked to him once or twice a day and he was gone within a week.

 

[namiieco]

Personally it never worked for me.

I would talk to them and keep tt 4 days at a time, making sure that they will still ping you if they want to move in the process. I find that the villager who move are pretty random and it's just by chance that villagers want to move. You could get an amiibo and kick him out if you want if you have them too.