Gulliver flies through the air in a UFO. Booker is not able to know if Gulliver is going to visit. He won't report any visitors for the day, and there will be no hints or anything that Gulliver is coming.
When Will Gulliver Pass By?
If you don't have Redd, Saharah, Wendell, Gracie, Katrina, Dr. Shrunk, or Pascal in town, Gulliver might pass through.
Gulliver always shows up right after you start the game. He will show up at the minute xx:x2 or xx:x7 (whichever comes first) once you have gone outside. If he doesn't show up at that time, then he won't be showing up that day.
How to Shoot Gulliver Down
To get Gulliver down from the UFO, you must run up to the top of the town and shoot the slingshot at the UFO. The UFO will come crashing to the ground, and Gulliver will make a crash landing in one of the vacant lots in town (a spot that has a sign and would have a house on it if a villager lived there).
How to Get a Gift from Gulliver
Look at the screen after Gulliver lands to try to figure out where he crashed, then go to that spot and talk to him until he wakes up (he will mutter some nonsense for a while). When he wakes up, he will ask you to go find the missing parts of his ship. There are five missing parts in total, each of which looks like a metal gearwheel. It is OK to save and end the game at this point; Gulliver will still be there. Once you collect the five pieces, bring them to Gulliver and he will give you a rare item in return. Then he will work on repairing his UFO.