I believe that molded plastic stuff is actually hardened setting tape. It gets very brittle with age. But if it's not original glass, it may indeed be some sort of molded plastic.
Have you tried asking at an automotive glass shop?
Glass shops ZERO (looking in/from the Upper Desert to the Lower Desert of Palm Springs,CA areas). There only suggestion is using a calking type runny mess stuff. Not what I want to use. There's got to be something easier or less messy out there.
