Mystery Man in Green Eggs and Ham

Ok, so maybe I've read Green Eggs and Ham a few times too many lately. But, have you ever noticed the "mystery man?" He shows up in the coach car of the train - the first time you see the train. You then don't see him for most of the rest of the book - you only see the woman and child in the train (or in the water, etc.). But, you see little glimpses of someone else that hasn't been previously introduced. A hand here, a hat there (mostly while they're in the water). I'm going on the assumption that the man in the train is indeed still along for the ride throughout the book, he's just ignored. It's as if he's having a cameo appearance and is then treated like an extra.

It's a bit odd to have read a book so often that I can almost read it from memory; leaving my mind free to wander and think about such things. Perhaps we need to go to the library more often.