The mystery of "whats in the box on tank-mounted DSHKs?" has bothered me for a good long while and I have finally found a picture where the box is open. Now, I might have been able to find the answer through a little more digging but asking the bearsite sounded more fun lol.
(Image below is with the box closed)

The thing inside of the box looks like a WW2-era reflector sight but smaller, which would make some sense because many of these roof mounted MGs are meant to harass attacking aircraft. However that doesn't seem right since those sights are pretty sensitive and the sights for dedicated AA DSHK setups are very different.

My other guess was that its some kind of periscope setup to allow the user to aim and fire without fully exposing oneself but the angles dont seem right for that. It might be notable that this feature is part of the tank cupola mount itself, and is not present in any tripod setups or any other vehicle mounts.
So like... what is it?
I found a YouTube link in your comment. Here are links to the same video on alternative frontends that protect your privacy: