System voltage when the engine is running are higher otherwise the 12V battery would never charge. Can be as high as 18V. So cars with halogen lights with just chop it down to 12V.

Here's a random video I found demonstrating the phenomenon. https://www.youtube.com/watch?v=82tFav8oGFI

Interesting, so they're using PWM to hold the headlights at constant brightness when the alternator runs. Wiring a capacitor in parallel with the headlights should fix that.