Output from a TV to a 2nd monitor
I have not ever heard of a TV that has this feature (I have encountered a few).  Some high-end monitors have this, it's called Display Port daisy-chaining.  As the name implies, it uses DisplayPort and not HDMI.  It's quite a hack; but, I think that your cheapest option would be to put a camera outside the booth looking back at the screen.  Amazon has some very good deals on decent performing cameras, look at Dericam.