This sounds exactly like what I want to do! Would you mind answering a few questions? How did you find the town in Japan to move to? Also, did you buy/rent an apartment, or was it an Airbnb or something similar? How did you pay for it - savings, or the odd jobs that you talked about?
The opportunity that arose assigned the city (Shingū) to me—it was the sister city of where I was living in the US. My partner taught English and she was given an apartment by the city. Airbnbs are available everywhere though. I used my savings; I don’t know the total cost but it wasn’t too expensive being in a remote area—as long as I resisted buying a pile of snacks from FamilyMart each day.