I figured out how the parking light circuit works, but it is very confusing. The switch sends a signal, probably to the BCM, rather than just mechanically removing or applying voltage to the lights.
If I rember correctly, when the switch is off, there is +12v on the parking light wire. When you tun the switch on, it connects that wire to ground with a resistance. The resistance varies as you turn the switch which is why you have one vlaue for the parking and another for the headlights. I also found that there is another resistance value to turn on the fogs.
I don't think I have that completely right, but it was along those lines. I found that I needed a relay to bypass the switch while the remote start was activated and it was going to be a big pain. I just decided at that point to get everything else working and I'd revisit it. That was a year ago and I still haven't bothered to mess with the parking lights! It's not a big deal for me at all really because if I have the lights on auto they'll come on when it starts anyway. I don't get the flashing lights when the alarm is armed, but that doesn't bother me either. Good luck with it.