AT NCL the fireservice do teach Airside Driving Courses... BUT
It depends which company you work for. When I was at Servisair, we had our own qualified trainer, but I know that some of the other companies don't, so have to have it done at the Fire Station.
I had to have my license renewed once, and I definately did my recourse at the Fire Station. IIRC the Airport Police and the Airfield Lighting crew were doing a refresher at the same time.
Its probably the smaller presences at the airport (Eastern Airways Catering, Emirates etc) that do their training with the Fire Station.
In terms of what you learn, its very basic, road markings, speed limits, height restrictions, driving around aircraft. Unless you're going to be going onto live taxiways etc... there really isnt much to learn, at least not at NCL. (Also the course at the firestation is largely theory, specialist vehicle training WILL be done by your own company)
RTG