You are doing the inverse of what you want. A Clipping Mask hides what is outside it, not inside. So what you are doing wrong is putting the mask around the wrong thing. Instead of one mask showing the middle, you need two masks (and two logos) to create a middle. You must either have two instances of your design, one of which has the top masked (revealing the top) and the other the bottom (revealing the bottom), or you must cut one logo into two pieces, which would involve, perhaps, selecting the 2, going to Type > Create Outlines, expanding the stroke on the rectangle, and using, the Knife Tool. I'm sure there are other ways. If you look at the screenshot of the Layers panel and artwork in post 1, you can see that there are two items labeled "box-design" and two rectangles, each of which is paired with one of the other, in which the rectangle reveals, not hides, half the "box-design". Apologies. This is far simpler than my attempted explanation makes it seem.
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