I've had one of these 'flamethrower turret' malarkies. The design was almost identical to yours. I found the most reliable way to activate and deactivate was to dispense with the forward-facing bridge altogether...
WWWWW
F B Wc W
F C W W W
F W T SW
WWWWWWW
So 'C' is a dragon-containing cage linked to a lever, 'B' is a retracting bridge, 'T' is a cage trap, 'S' is an animal stockpile accepting only dragons and 'c' is a kitten. Aw. The bridge is retracted. When guests arrive, release the dragon. When the party is over, open the bridge (B) and your scaly friend will race round the corner to frazzle the kitten, becoming captured in the cage trap.
I've had mixed results with it. I found dragons pretty unreliable in terms of rate-of-fire. Perhaps it's worth testing a dragon's reactions with various victims willing subjects. I mean, if it transpired that they had a particular dislike for kittens, say, you could fling one of them into the mix whenever the dragon gets 'flame-out'.
Of course, magma is more practical for such an application, but it just doesn't have the 'Wow' factor.
Edit: Maybe it's worth having the 'turret' backwards-facing. That way the dragon would always get the drop on the gobbos, or what-have-yous, as they wouldn't even clock the dragon until it was way, way too late