I was able to find the cable. It looks like there is adhesive in three places: at the end of the cable by the connector to the display, on the silver grounding piece, and at a point a little less than halfway from the display panel end where it has extra fabric, presumably to allow it to be stuck down to whatever. I will dig out one of the displays from the mystery box and see if I can figure out what it is supposed to stick to.
You might be able to use regular double-sided tape, but I’m not confident that that would hold up. Contact cement might work, but could be messy. Or you might be able to use “regular” tape of some sort to tape over the cable and to whatever it is that it supposed to stick to. Maybe the display panel itself? Apologies that this is a lot of guessing. I’ll reply back when I have looked at one of the displays so that I have a better sense of how it goes together.