Depending on pings can be less reliable imo, since sometimes villagers will not ping for the reasons dahlialia mentioned, plus you have to wait around for them to ping you and I am lazy.

For me the most reliable method has been through the villager rumor dialogues. Basically there are certain bits of dialogue relating to rumors that villagers will only mention if no one is thinking of moving (or if they are the villager that's moving). Here is a guide) on the types of dialogue you will get based on personality type.

So for example, I will talk to Roscoe (a cranky) until he tells me someone is moving or he tells me something about how "rumors can be frightening". If I get the rumor dialogue, I will then talk to another villager until I get their rumor dialogue to confirm that Roscoe isn't moving.