I'd go longer than 10-15 seconds, probably a minute or three. 10-15 seconds, the car may stall before the carjacker leaves your sight, and is still in shooting range.
You'll want to make the cutoff semi-permanent too. You don't want it resetting if the thief turns the ignition off/back on, which a simple timer would do. Maybe wire it so it blows the fuel pump fuse when it triggers.
There could be safety issues as well, such as if the car stalls in an intersection. I don't care much about the welfare of the scumbag that stole the car but the car itself could end up wrecked... maybe a better solution is to have the hidden switch trigger a circuit that kills the fuel pump after the car is shut off. Thus, the jacker gets away, stops for a beer (or whatever), then they get back in and the car won't start. Maybe combine that with a timer... fuel gets cut off next time the car is shut off, or after 5 minutes, in case they just keep driving.
I've often had ideas for things like this too. If I were to do it, I'd have a little fun with it (using a microcontroller). Perhaps I'd give a warning by stalling the engine but allow it to be restarted once or twice before it dies completely. Or even modulate the pump so that the car starts or runs like an old jalopy. Or have it gradually kill the engine by cycling the pump on and off, with the off intervals increasing in time, so the car sputters, coughs, and dies. Make the carjacker think he got a POS and he leaves it on the side of the road.
Or for some real fun: after the car stalls and the thief tries to restart it, have the lights start flashing and the horn blowing. That should get some attention.