Let's say you get a new villager moving in but you don't introduce yourself do they still move out when you time travel to get one of your older villagers to move out?
Apparently the newest villager won't move out until somebody else does....don't know how true it is but it seems pretty accurate with my town at least
In which case it wouldn't matter whether you introduce yourself or not as they should go anywhere before one of the old ones leave anyway.
I heard that ignoring a villager after you introduce yourself on the first day makes it easier to get rid of the villager,
given that he/she is not your most recent villager.
But yeah, even if you don't introduce yourself, they will still move out eventually.
The last villager to move in can move out, even though the older villagers usually move out first. And, yes, ignored villagers will eventually leave. I always recommend befriending them in order to get them out faster.
I've read on some guide that if you don't greet them the day they move in, it'll take a very long time for them to move out.
buuuut I don't think this is 100% true.
Ignoring really is the best way to get the last move in, to move out (in my experience)