Most likely is the Mode Door Actuator Motor is bad (shorted by too much grease from the factory). I replaced all four door actuator motors on my 2005 Yukon as it had the random blowing Hot/Cold thru passenger side and driver side. When I opened all four OEM motors , their position feedback contacts were All shorted by excessive grease from the factory. I have owned my Yukon since new, and it had the problem since new. There is much info on this online, and it should have been a recall by GM. It affects All GM products from early 1990's thru late 2000's. Your mode door actuator is attached to a cam that selects direction of air flow to floor, dash, defrost (windshield for defrost) and is likely stopped working in a partial cycle where full air flow is Not directed fully to the defrost mode. I bought aftermarket motors for all but the Mode Door as I wanted the Cam along with the new motor. It was the cheapest at approx. $58.00 on amazon. The other three aftermarket motors were under $30.00 each. From GM each motor was over $160.00 each. Mine has been working Great now since replacing all four motors last January 2019. Best of luck with this as it was a painful experience.
montegutman