Anyone ever solve the Fusion AC blowing hot or cold based on fog lights being activated issue?

Hello,

I'm new to the forum and I'm looking for some insights into an odd problem. I've got a 2011 Fusion with the 4 cylinder and manual AC. The AC started blowing hot (not just not blowing cold, but only blowing heated air). I can hear my blend door humming as I change the temperature, so the blend door is working. The only thing that works is this quirky advice I've seen on several forums suggested by several people: keep the lights and fog lights on and the AC will stay cold. It sounds weird, but I can confirm that this trick does work. My AC blows consistently cold only as long as the lights are on. My question is: does anyone have an explanation for this and will replacing the AC control module address this odd electrical cross-over?

Thanks for the space to pose the question.