I'd msg @Andyjr1515 for his take on the matter, and glue choice.
Its a crack rather than a break, so no real alignment and angle issues, plus a nice bit of extra volute wood for strength in the vacinity...
ASAP While the tension is still on, some titebond(?) or most suitable - be nice and warm and runny this weather - to wick in all the open gap. Rather than looking to open the gap again for the glueing.
Then off with the tension and a good clamp... (i've seen inner tubes wrapped around things, then pumped up to apply conforming pressure if no decent clap and packing) - how long? 48hrs?
As mentioned previously, no lacquer finish, so a little bit of sanding, wire wool 0000 to remove any glue ooze and a dab of oil or wax!