Convertible top

Oh, well, you are going to need that track. It seems to be a generic extrusion, but it is curved to match the seat back. One reason the top may not go down flat is if an aftermarket top used a heavier material than stock. My old car (light blue 'cuda above) used a pinpoint grain material. Leather grain vinyls seem to be heavier and less flexible. Or it may just need a little adjustment to the frame.

68-69 convertibles used the leather grain top material.