I dunno mang.
Lojack's own manual mentions the need of a constant 12V power supply.
Originally Posted by LoJack
I was told that the configuration of my LoJackŪ may vary depending on the year, make and model of my car. What does this mean?
Different types of cars have different power management requirements. In particular, some newer vehicles do not have a constant 12 V power supply for LoJackŪ units to operate from reliably. In order to ensure continued functionality of our LoJackŪ Stolen Vehicle Recovery units, the configuration of our products may differ to allow for these vehicle variabilities.
So, if the OP claims that no other electronic devices are installed on the car, then the logical conclusion is that THAT is the tap for the power for LoJack. There are other references found through the wonderful Google in regards to a 12V power supply needed to charge the back-up battery.