Great find!

TonyC's idea is my first thought, just leave it as part of the whole antique appearance.

Beyond that, the defect cleanout and prep, then a patch install would be the next logical step. Disassembly and patching from behind would be the ideal, but most challenging. Only thing I can add is maybe scavenge a fill piece from somewhere in the back so you have a piece of wood with the same finish and general grain pattern.