IANAEE, but I'd use a normally-closed relay. My terminology is bad, so I'll describe each connector. Tie the ignition line of the car to the lead of the relay that activates the switch. Tie the LED in series with the lead of the relay that is turned on and off by the relay and the always-on power from the car. Tie ground to ground.

When your car is on, the ignition line is on, so the relay is activated, which means that the circuit is open (that is, the switch is off). When the car is off, the relay goes back to its rest state, which is closed, which means the switch is on and power flows through the LED.