I've never had a Hat Man experience but the phenomenon intrigues me. From all accounts it sounds like something very ancient and powerful, but not evil or malicious. Which suggests to me an entity that may have existed for longer than humans. However, the wearing of hats especially of the Hat Man style is relatively new. Did it adopt this look as a way to mimic the humans it visited? If so then what did it look like before these kinds of hats were a thing.
I'm also wondering if it's not actually a Hat but a part of whatever this thing is. There have been depictions of ancient entities throughout human history that have animal like features such as pronounced brows or horns. Could this Hat Man have physical features we don't recognize or understand? What looks like a horned head to someone living 1,000 years ago look kinda like a fedora to someone living today?