Here's an update on this. First, here are pictures of the project
I called the dealer and they said that it is fiberglass and can be patched like any other fiberglass.
I called Jayco and they said that it is a product made by Filon. I went to Filon's web site and found out that the material is called Glass Reinforced Plastic, and that it is pretty close to vinyl that has been reinforced with glass much like fiberglass.
I found another manufacturer of Glass Reinforced Plastic who provide instructions for repair, which look just like fiberglass repair.
So the dealer was basically right, and I just need to patch this like fiberglass.