any change of the state on those two pins?

if the trailer module supplies power to the lights from the pin 3 (designed to power rear fog light of the trailer, not the fog lights of the car), the trailer module must respond to change of the voltage on the regular fog pins (pins 10 and 12)

Also, if i remember correctly, there was something in the programming file about rear fogs - i know the original write up did not mention any programming changes but could it be that the LCM needs to be "told" about activating the rear fogs?