What is the best glue to use to fasten a strip of Styrene, (ABS Plastic) on the inside and outside of a fiberglass cowling?
Personally, I wouldn't use ABS plastic.
If the cowling is fiberglass, I would first find out if it was Epoxy or Polyester. After determining this, I would use an identical stripe of the same fiberglass material bonding the pieces with the same chemical material.
I prefer Polyester but mant modelers like Epoxy better.