Or are their simply no tickets exclusive to Gatwick Express only?[/quite]
Back when Gatwick Express was a Company there were, but not any more as far as I know.
I was fully expecting Gatwick Express trains south of Gatwick to be more expensive, like the HS1 from Kent is but they are not.
HS1 trains are not more expensive, and the NRCoC does not allow this as far as I can determine. The HS1 route is more expensive. It's perfectly valid to have a Not HS1 routed ticket and use a High Speed train on the 'classic' part of the route (e.g. between Ashford & Folkestone)
They are the same price as any others. Given that they are nicer to travel in and less busy, this fact surprised me.
However I was also surprised to find the Gatwick Express rolling stock stopping at Clapham Junction once upon a time. This led me to board a gatwick express train once, during some major disruption on the network and say to a guard on the train but I thought the evening Brighton bound Gatwick Express services stopped at Clapham Junction. To which he replied no. Little did I know they were using the same coaching stock for other services that were not Gatwick Express. No wonder I got confused. Fortunately I didn't need to get out at Clapham Junction.