Should be a gasket of sorts. Probably thin rubber? Like a piece of an inner tube, die-cut to fit? The ones on my '67 Newport have body paint on them, on the outside.
"Trunk rust" can happen from the various temp swings with condensate being trapped under the solid vinyl trunk mat. First time I pulled the one up in our '66 Newport, I was shocked to find moisture there. Back when it was about 6 years old! Hadn't eroded through the paint on the trunk floor, though. Take the mat out, dry things out, leaver it out and do a water hose test. Also look to see if you can see the edges of the gasket I spoke of, in the gap between the extension and the end of the quarter panel, for good measure. Replace the mat with a carpet that doesn't have the clear rubber coating on the backside of it. The factory trunk mats had serged edges and were the same size as the vinyl mats.
Check for evidence of water in the tail light lens, too. For general principles.
CBODY67
