This thread references a TSB which may apply.
https://www.camaro6.com/forums/showthread.php?t=475080
I don't have a V6. But it appears, like most cars, you have 2 radiator fans. A good first line test is to open the hood with the engine on and A/C on high. Most cars default to the high fan speed for both fans when the A/C is on. You say the fan is running, but which one?
Although wiring may be the problem, in my experience is it either the fan itself or the fan control module.