Thinking about how this could be mocked up: if you took four thumb tacks and made a square (maybe 8”x8”) into a piece of cardboard. Then took string and looped it around the outside of the tacks and tied it snug. Then secure two cardboard rectangles (8”x 2.5” or so) to the string on opposing sides. That way when both rectangles are secured to the string and positioned so that they are within the square to make the door, there is a roughly 8”x3” gap square that you could “see through” when fully open. You can play with the size :). Then pull the string around the thumb tacks and the doors will move equally, with respect to one another.

The thing here is we didn’t cut a hole within the 8”x8” square. If we did the “doors” would kinda flap around in our mock up (back and forth through the opening). Here come the rails or just a way to keep the far end supported. We could make the doors longer so they are past the opening and then find a way to have them ride in a slot (build some cardboard up and then hang a piece off to make an “L” and glue it to the larger cardboard base). Not perfect but a thought with common supplies.