I’ve always used the 3m black super seal adhesive for weather stripe in a Cougar without issues. Did my trunk seal about 6 months ago on the 67 GT. I’ve had it open for About a week fixing the turn signals. And the seal fell off 
is their a better product I should be using? New seal maybe I should have wiped it down with prep solvent first.
3M makes a wonderful contact cement P/N 1357 for exactly this purpose.
I have used the same 3M product Royce recommended. Never had one come off with out a lot of work.
I’ll pick some up today and give it a try.
none of the auto parts stores have it around here. had to order some and will get it Monday.
Brian, Check in to a building supply or paint supply store.
I get it from https://skygeek.com
It’s all over Amazon too:
https://www.amazon.com/3M-Scotch-Weld-Neoprene-Performance-Adhesive/dp/B00HLSUO5A