Muntins, muttons, mullions have heard it called all three. I have done hundreds of windows and a lot of woodworking. In fact I did a podcast dedicated to the repair of this type of window and also covered modern windows. We did no, unfortunately go into repair of the muttons.
The three approaches I would consider, in order of first to last.
1) If the wood is solid, and you have all the pieces, I would just use some Titebond III woodworkers wood glue and try and glue the pieces back together.
2) Use parts from a salvage or discarded window. If you come through PA I'll be glad to give you the window I used when doing my demo of how to glaze, you might be able to salvage parts from it.
3.a) build new parts. You do not have the tools to build this part. Not olnly would the tools to do it properly set you back a huge penny you would need a workshop to contain them all. Off the top of my head - Router in table, table saw. OK, I could build it with those two tools and the correct router bits.
3.b) You could maybe find a well qualified woodworker, give him/her the broken piece and ask for a price to duplicate the piece in the appropriate length. If going to that trouble I would also have him/her install the wood into the frame.
My show on doing window repairs is at