The first strategy I tried was to follow one square around, staying connected to it, and forming other connections randomly. I suddenly realized I was following a marriage strategy.
This is where I found the invisible man:
It was on the level where you begin on one side of a deep, narrow hole and some other creature (I often see blobs or bats) on the other. When you drop to the bottom of the hole, you land on a platform 3 squares wide.
Anyways, from that platform, if you fly up and over to the right there is (sometimes rare) monster in that dip. I noticed that it looked empty one time, so I thought I'd check it out anyway. It wasn't empty after all, there was an invisible man.
 "I Am An Insane Rogue AI"){kind=icon}
 "Castaway"){kind=icon}
 "Love"){kind=icon}
 "Great Dungeon in the Sky"){kind=icon}
 "Everybody Edits"){kind=icon}