While TTing a day at a time to get more bushes from Leif, I noticed that one villager would ping to move when I did a certain thing.
That thing is
Play a day normally, talk to everyone, do daily chores like money rock, etc. Then save and change the time to 6:00 am the next day. Don't do anything and save again. Change the time back to normal. After this, someone would usually ping me to move as I'm walking around town. This is just from my experiences, so I'm not sure if it'd work for you too.
He's actually cool looking... better than most of the mice.
There is a method of tying forward six days and back 6 days, you go around and get someone to ping you each of those days, if it's not Limberg then stop them from moving and save. There's a few more details I think too, just don't remember atm.
If you time travel, TT 2 days forward, save and quit and then TT two days backwards and run around your town until someone pings or talk to each animal a few times until one of them tells you that someone is moving.
If not, ignoring them for a week works..that's what I did before.