With the release of Ron Cobb's designs from The Last Starfighter and a few photos (finally) from the film, this elusive prop can at last be reconstructed.
Have you identified the part above it? Looks like it might have been the same manufacturer only smaller.
To me they both look like mounting clips. The part you identified being the female end, the male end would have something that would push the silver disc on your part down exposing the slide rail to hook your item onto. Not sure if I explained that well, but yeah.