Can we get the material and the backing board you want to use? Makes a big difference. Vinyl and backing board is kind of a open area.
Weatherstrip adhesive works great as a contact glue or if clamped when drying, it adheres to most things very well.
I used Weldwood contact cement to cover my headliner and door panels. Both were made of fiberboard and I used vinyl from Hobby Lobby.
If its where exposure to temperature changes or moisture exists, what ever you use will break down in 5-7 years. If you are redoing something that has already been done before, you need to remove as much of the old adhesive as possible, or it will cause the new application to degrade faster.