During my high school days, we made a project similar to your concern. The project was building a simple direct current buzzer where there the coil and contact points and armature were in series to the battery and switch. The coil was made up of magnet wires. I wounded two sets of coils, one was the primary made of bigger wire and the secondary was made of fine wires. This resembled the ignition coil of a car.
This is how it works. When the switch is closed, the current flows through the contact point, to armature and the primary coil creating a closed circuit creating an electomagnet. The magnetized core then pulls the armature, thus breaking the circuit. When the armature returns and connect to the contact point, the circuit is closed again, the coil is magnetized, thus having a continuos on and off cycle. This creates a pulsating DC in the coil. The pulsating DC creates magnetic flux and transforms the battery voltage to a high secondary voltage depending on the ratio of the turns between the secondary and the primary. The higher the ratio, the greater the induced voltage in the secondary. However a capacitor is needed between the the contact point and the armature so as to prevent the contact point from damage or pitting due to induced current.
I just dont know if a 12 volt dc door bell placed in series with ignition coil and battery will work. If it works, this will serve as your on and off machine to create pulsating DC to the ignition coil.