A/C short cycling

I appreciate any help you guys could give me as i am unable to figure this out on my own.

It first started by the AC staying ON when i would turn off the truck, and the only way to turn it off was to either disconnect the battery or disconnect the blower resistor.
Afterwards the AC would blow cold air normally than out of no where it would stop, and a few seconds to minutes later it will blow cold air normally again. The AC would only work on the max setting.

To turn on the AC i had to connect the resistor to the blower under the dash. I was told that the Resistor was faulty so i replaced it but it kept doing the same thing. i had check the fuses and the blower fuse was burned so i replaced it. but it kept doing the same thing.

A few days ago i replaced the blower fan under the dashboard and it worked the only problem now is that it only stays on when its on the max setting because if its on any low setting it will stop however you can still feel the cold coming out but barely little few minutes later it will start blowing cold air.

The clutch or compressor engages and i can see it run.

My vehicle is a 2005 GMC yukon 5.3 with automatic AC.

The A/C compressor is mechanically driven. You turn the engine off and the compressor stops working.
I believe you might have problems with the blend doors. Turn the blower on a medium setting and try to re-direct the air to various positions, re-circulate, feet, dash and so on and see if that makes a difference and the airflow responds to your setting. Oh yes, with the engine running and A/C on, of course.

Maybe I don’t understand the problem but I’ve had two similar if I hear you right. If the blower stays on all the time until pulling the fuse or battery cable, when that happened to me it was the blower control module. $25 at the junk yard. When the air conditioner would periodically turn off and I’d have warm air blowing and other HVAC issues, it was the HVAC programmer. A computer box with vacuum lines etc. going to it. Freon level was fine. I don’t remember what I paid for it at the junk yard but somewhere around $100. I followed the diagnostic procedure in the repair manual though so that would be the place to start.