The location of the crack is a bit suspicious. I would certainly put some sideways pressure against the upper limb with the bottom limb held in a vice to see if the wood opened up across the top of the shelf and on the belly side. Even if it is a crack, you could take a tiny drill bit and put a couple of 1/4 deep holes down into the crack and then fill them with Loctite 420 or 720 superglue (I forget the number). That stuff has excellent wicking properties. If no crack shows, then it would be a quick fix just to stabilize the glass overlay where it is cracked.
That looks like a clean old Polar