I have looked at a bunch of websites similar to this one, and all of the answers are rather vague. I have collected 3 lamps now, and I have no clue where to find Wisp. I am pretty sure that it has to be after nine pm, but, other than that, I don't know how to find Wisp. Where should I search for him? What day of the week? Does weather affect when and where to find him?
According to this website:
He will appear in your town on a random day; any day of the week. The only time that you may find him is when it is late at night. However, there is a surefire way of knowing that he is in your town that day. If you see a genie lamp laying on the ground near a tree or a building, that guarantees that Wisp is in your town tonight. If you find Wisp before the lamp, then you must find the lamp after you talk to Wisp. If you find the lamp first, search around for Wisp - he is usually found near the beach but could be anywhere. Eventually a text box will pop up and Wisp will say "Psst ... come here." You will then have to play a game where he moves and you have to find him. After you catch up to Wisp yet again, he will say that he is scared and asks you to meet him in your attic. Proceed to your attic and rub your lamp. Wisp will appear and offer to grant you one of three wishes.