What we don’t know is what is on the inside of the box, possibly expanding with the weather? I would not use Cascamite for this job – there are better, more modern – alternatives that may actually be waterproof.
Unless it is easily pushed back into place, there may me considerable sustained force on any glued joint to end-grain. Just look at the surface area of the joints (which would be glued when made), compared to the ends where you can get glue into the joint.
A stretcher, inside the box, to form a compartment, is likely needed to keep it in place. Unless the box is dismantled and re-glued.🙂