He knows that he’s perfectly sane.
In fact, he knows a lot of stuff that they don’t. He knows they are trying to find out about, you know who, him! But they won’t find out. They’ll never know where he gets his information from. He can see how amazed they are by what he can tell them in his sessions, but he’ll only tell them so much. He was only allowed to keep a few personal items in his room. Things they deemed were safe. Strictly speaking, the rules don’t allow their guests to have access to certain items, such as shoelaces, belts, neckties, and bed sheets. What they are most careful about is denying access to any sharp objects. Naturally this includes mirrors; glass can be broken.
Ha! They let him keep his grandfather’s old pocket watch. They never checked the back. They never even saw that it opened! They don’t know his secret. They must never find out about his secret.
They must never know about his doppelganger who hides in his tiny mirror…