A villager in boxes just means they're packed up and ready to move. They will give you about 5 days notice usually.
There's not really a way to do it faster as its random but you could use the time travel method. I tend tt day to day as I have most of my dreamies now so I don't want to lose them. I think there's a faster tt method but I'm not quite sure how it works. Although the one I use I've always had success with.
Alright, thanks for the help! I'm probably gonna skip 3 days at a time and just check if Fauna wants to move out and just skip ahead to the moving date.
I just got her ping! though it said she was moving out "The fourth of this month" but it's the 30th so I'm guessing the fourth of next month? Anyway, just respond and I'll time travel to her moving date so you can come and get her.