Per the FAA web page there are only 4 AMEs in Japan. Two up around Tokyo including the one JB referenced, one in Kawasaki and one in Kagoshima. The FAA has a search function, if you search for FAA AME it should come up. Select AME and even though you are just looking for a third class select first, second and third class medicals. Doesn't look like anyone just does second and third classes in Japan.