"unfortunately" it is so simple, nearly anyone I have told yet, believes it.
There is the driver that steps-up the battery voltage to the roughly 65 V the HID bulb needs and - mounted parallel - a Voltage Multipier (Greinacher or Villard cascade)
As long as the arc does not work, the power goes to the Greinacher, till the voltage is high enough that there is a strike.
Again the arc does not start - the next spark form the Greinacher
every time there is a strike, the gap between the contacts "looses resistance" and at some time the arc stands,
more and more power goes to the normal step-up and the HID "goes off"