Not to completely throw cold water on the idea - I believe it is possible to get residence visas in the EU based on being retired. That said, I don't know if this is the case in Greece or not. Immigration is one area where the individual countries are loathe to give up their ability to call the shots.

Generally, you need to contact the consulate in the country in which you are currently resident for details. And don't be surprised if the Greek Consulate in Thailand has no clue how to deal with US citizens. They may require all sorts of "proof" of your financial means and social insurance, and even then you can be turned down for what appears to be no reason at all. But if you don't at least ask, you won't find out.
Cheers,
Bev