Is this an expensive instrument, collectable, or a CBG? Hate to give advice on something best left as is for value sake, but if something you want to use and have repaired, personally, since it's split all the way through, what I've done to similar repairs, is to open up the split with a saw blade/sandpaper and make an insert to slide into the opening made of the same material, glued in place, re-file/sand/drill as needed, using the same wood material will make the repair nearly invisible.
Other headstocks in worse condition I've made a laminate headstock top plate, like the way you can find a Mahogany neck/headstock with a Rosewood top plate...ie; Martin, etc
thanks for the reply , but its a rough and ready CBG, just want to keep it playing
Then I would slightly enlarge to slot, glue in a piece, I wouldn't just try and glue it back together, seems like the simple solution, but if there was enough stress from humidity/expansion, gluing it as is and trying to apply pressure might cause a crack elsewhere, but even simpler, would be just to add wood filler, sand and reassemble, since it cracked, the pressure is relieved and shouldn't get worse, and the machine head tuner will also help secure it.
Ahhhh, this guy...
looks like the grain was running the wrong direction on your wings for the headstock, this contributed to the split, you may get more, if it splits again, make a one piece face for the headstock and glue over the headstock, may need longer tuners or shave down the headstock afterwards.
but, try a simple repair first, may get many more years of enjoyment without all the extra work.
Thanks for the reply
I second the glue it and clamp it fix. I like Darryl's recommendation of adding the plate to either top or back since the grain is running the opposite way as Richard pointed out. That will reinforce the headstock against more splits later.
I don't know guys, typically, I'd agree with you, glue and clamp, but, you'll be reapplying the pressure and it will want to pull apart again, the glued joint won't, but right next to it might pull apart since it's got grain working against it. I'd still just open up the slit and glue in a piece of flat material, leave it in it's relaxed position, or as suggested, a face plate, or plate on the back. I could be wrong, only an observation.
That's why the plate is a good idea, to keep the problem from reoccurring in that spot or another. The plate would absorb the stress and possibly help with tone and sustain.
It's fix and add plate or time to strip off the wings and put new ones on with the grain in the right direction and possibly harder wood.
Your idea of opening the crack and filling it with a sliver of wood may put more stress on the wood around the hole and cause a new crack. Also, it may make the hole bigger causing a loose tuning key to rattle.
All the tuners used to be on one side. A crack started in the same place as the one shown above. The crack migrated to the other side of the hole. So I had to reshape the end of the headstock and move the other tuners to the the other side.