It appears as if there is a fair amount of thickened goo on that board now, likely other repairs and/or fairing attempts.

I can see just how that broke, huge point loading on a couple of square inches of 1/16" grain long veneers. Not much "purchase" power.

Michael's idea sounds reasonable and easy enough, though I'd opt for one big threaded rod then a couple of smaller ones, running perpendicular to the break. Maybe you could use the inside edge of the bolt to absorb the loads of the pivot with careful positioning when drilling the hole.

Another more reliable fix would be to "let" a notched piece of metal into the board at this location, maybe some sheet stainless on each side of the board, epoxied in place. It would absorb the pivot loads and keep the wooden pieces together too.