(Edited this post because i noticed some things that was overlooked initial observation.)
What im about to offer isnt advice but an observation. One of my purchases of a case that came with a free shamisen that had this same issue.
Their solution? Well for reasons unclear to me, they replaced the whole tail piece and re-glued the joint. Ill share some pictures but it looks like they drilled two holes. There was still some glue in the holes so they didnt use nails. Theres glue on the surface of a cut piece thats attached to the “new” tail piece. I guess they did this to make the joint more complex/add surface area? And they wrapped it in cordage at one point.
I dont know if the cordage served as a clamp for the glue or if it was permanent, it arrived broken l. You can see the marks left behind on the wood from it.
I wouldnt recommend fixing it like this; afterall, it broke a second time. Im generally against the damage of the original pieces by drilling into it a cutting section, but it is quite minimal and dont know what is common practice in this kind of repair. If you have the option, send it for repairs. But i think it is worth mentioning/documenting this.
My (unqualified) advice If i were in your shoes and didnt care about the potential consequences, I would carefully remove any existing glue and just glue it back together using a clamp. I would try solvents before sanding/filing and try to add some cushion for the clamp so you dont mark up the wood. Use something like wood glue and not something that would be more difficult to remove like superglue.