The original glue was a formaldehyde based phenolic, brand name today "Resorcinol". It was a great choice because the bond was stronger than the wood which surrounded it. Sure enough, in the photos above, it's the wood that failed and split and not the glue.
It's really unusual to see damage as extensive as this. There's going to be no way to properly stabilize and repair it. The same glue could be forced into the cracks, but this would yield an unsightly mess. The splits mean that the stock's original dimensions are lost as well.