From what I've heard or experienced, talking to the a bunch in a day for a long time makes them more likely to leave than ignoring them. Accidentally lost my fav villager that way (rip Phoebe </3)
Apparently if you gift them exotic fruit or fossils every day, they will give you their photo and soon after ask to leave. I saw that in a group on Facebook and I tried it and it worked. Haven’t tried repeating it yet.