A shrink in Nippon, eh? Mmmm...
As another poster commented, the Japanese do not like admitting they have any mental issues. Culturally, seeing a therapist is just not cool.
However, that said, a friend who lives there and teaches English said that many of his adult students are in his class because their (Japanese) doctors recommended taking an English course. Why? They would mention to their doctor about feeling stressed, etc., and the doctor would recommended that they take an English course taught by Westerners because (paraphrasing) "Westerners talk about personal problems all the time and don't mind listening to people moan and complain."
Personally, I think there could be a market for it. I'm not sure if there are any legal requirements are for being a "therapist" in Japan, but if discreet one could solicit business by advertising so people don't lose "face." The English class above is a perfect example. Sort of like ordering an inflatable girlfriend through the mail knowing it will be delivered in a plain wrapper.
Get your work visa as an English teacher with "talk therapy" [ahem] being part of your methodology. The Japanese are pretty good at figuring out things are not always as they appear, and in one of the densely populated areas I can imagine word-of-mouth might travel pretty fast if you offered them what they were really looking for.
As for not being Japanese, I think that is an advantage. Most people are more comfortable talking about problems with someone who is different from them and not someone local who they, or their friends, may know.
If your desire is to sincerely help people, this could be a good thing.
JMO. Good luck in whatever you pursue.
