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

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.
I'm probably confusing the newer ****.
Probably is white/beige with age. Ive done and do a lot of work ..on a lot of cars. The little things like door panel undersheeting ..
If it were mine I'd be comfortable using either...uh how about blue painters tape..lol eh nah.. I wouldnt go that far. Jk