Not an expert but I've had several 65's. The 2 dr post body I had was a Belvedere (Bel 1) and had the thin trim. I had a 4 door car that was also a Belvedere (Bel 1) that also had the thin trim. Most but not all 4 dr cars were the Belvedere II model and used the wide side trim typical to the H/T and convertible cars. I don't know if it was optional equipment or standard. I do know it and the attachment clips are hard to find in nice shape. If you have it and it is nice I would use it.
I think most delete the trim if its incomplete do to the cost of replacement.