What to use to replace the string with putty on it to hold the plastic

Stuff in my 67 looks like butyl almost ...you could use a skinny strip of black butyl tape..then the black tape...which is wide like duct tape..but not.. similar to wide black masking tape, but not quite..lol
My one family owned 67 dart had white dumdum like material holding all plastic in place, much of it is still flexible.

The bottom tape was black looked like masking tape and had long ago hardened to being fragile and non adhesive.

I assume it was a tape that was semi water resistant.