Daytime Running Lights

I recently helped someone install some daytime running lights on their car.  The kit is pretty simple and only contains two lights and a controller box that I've shown below.

Installation Instructions

As you can see, installation is simple, two wires go to the battery, two go to power the lights, and one connects to the positive terminal of one of the headlights.  This is to comply with local regulations in Australia.  When the headlights are on, the Daytime Running Lights (DRL) have to be off.  The wire that goes to the headlights sends a signal back to the controller that lets it know if the headlights are on or off.  If the voltage on the line is 12 V turn off the DRL's, if the voltage on the line is 0 V turn them on.  This raises an interesting problem though, the system is directly connected to the battery, so how does it know if the car has been turned off?  With the car off there is 12 volts on the battery terminals and 0 V on the headlight wire.  From what I've described so far, the lights should be on, but they aren't.

So what's missing.  The controller box can somehow tell whether the car is running, how's it doing this.  The first couple of ideas I had were ridiculous and complicated. A piezo sensor to sense the engine vibration, or sensing the voltage droop of the battery when the alternator kicks in, but how does it know the car is off?

After thinking about it a bit more I think I know what is happening.  When the car is running, the alternator charges the battery, and when it does this there is 13 to 14 volts across the terminals of the batteries.  This must be how the controller knows the car is running.  12 volts isn't enough to turn the system on, it can only be done with the higher charging voltage.  I won't be able to test my theory because the unit has been installed, but it seems to make sense.  I like the idea, it's simple and elegant, keeps components to a minimum, and makes after market installation easy for someone at home.