Update. I installed a brand new fan control module 2 days ago, and voila... problem solved. Fan runs when ac on. Fan runs when car needs it to. No rad light. Everything is great.

2 days later.... drive car 20 miles. Car overheats. No rad light. Fan still running. But the car still overheating while driving. When idling the temp gauge begins to drop. So no rev = happy car.... rev = slowly climbs to H on gauge. It’s important to note that when I pull over or drop it into neutral and coast, the gauge shows it’s cooling... within 45 seconds it’s back to ideal temps. Shift into gear and drive, within minutes it heats up again. Thoughts?