I'm with Rob and Nick.

If it is on an area that can not be seen from the interior, mix up some dooky smootz of epoxy and sawdust and spread it in place. You can check the coverage by shining a bright light from the back side and look from the other side. You will be able to see any thin spots as the thin wood will look luminiscent.

If you don't like that approach, glue or epoxy some strips over that area on the interior, plane, and sand. It will look great. I have done this on the exterior in one spot and no one can find the area of repair.

Tom