Rick, i also run a 2012 RT in Germany and mine does just the same since the first day i got it.
I even was told by the dealer when i was instructed that day i picked up the Spyder there, that a vapor smell ist normal after riding.
Every time i stop the machine in the garage and come back several minutes later there is this (sometimes intersive) vapor smell.
It may also be, that there is something defect in addition, like the others allready wrote, and you should carefully check this,
but if you cant find something wrong, i just think thats the normal behavior of your bike.
Let me try to explain why (using pictures from the repair manual) i my not perfect english:
From the EVAP-Canister (1) there is a hose (5) going down to the bottom of your bike.
You can see it there comming out in the middle of your bike.
In normal state, this is where the vapor smell comes out.
After riding and looking at this hose afterwards, you can even see the petrol vapor coming out of the hose as glimmering air
(maybe flickering air is the better word, i dont know).
View attachment 198646
The function of the EVAP-Canister is descriped in the repair manual like this:
View attachment 198647
But what happens after riding, when there is of course still petrol in the EVAP-Canister?
Its evaporating through hose (5) to the outside and the bottom of your bike till its gone from the EVAP-Canister.
So, thats why you (we) can smell this like descriped, and thats also why this is simply normal because of the circumstance our old bikes are built
(new ones are not built like that any more and thats often the reason owners of new bikes think there MUST be something wrong with a bike smelling like that).
Maybe this helps you to arrange the situation a little bit better and avoids searching a malfunction where no malfunction is ...
Regards
Michael