I add my voice to those recommending the use of the old hot glue
for organ repairs.  I spent about ten hours with a Dremel tool,
cursing the person who rebuilt a German fairground organ pump using
what appeared to be some sort of rubber glue.  It had penetrated the
wood to a surprising depth and resisted removal mightily.

Don't use modern glues, they are intended to be permanent.  You might
be the next to separate the pieces.

Scotty Greene - DeBence Museum