You begin by talking to the man standing outside of a swingset on Route 2. If you ask him what's wrong, he'll tell you that his Alolan Meowth is missing. I spent a bit too long looking for it! Just head west to the motel, and approach the front of the truck. Hit A when the prompt appears, and then choose to look away from the Alolan Meowth. Return to the man for a reward and a cutscene.
Oh wow I must have skipped that! I think I'll give that a try once I return to the first island again to get that one totem sticker that you need a fishing rod for lol.
I believe it runs off south, past a woman? I read that somewhere. Unfortunately, I haven't done this myself so I can't be certain.
There a woman right next to the fence and there's a gap and a sparkly bit. She says that she saw a meowth run past and if you like the sparkly bit and say "purr purr!" It ll finish the quest.