Air conditioner does not work properly

I would trust your diagnosis first. Usually if the compressor works at times, it's working, ... Period. There ARE things that can cause them to work intermittently, but that is rare, and it won't be so consistent as what you have observed.

Your description suggests there's a problem with air flow through the condenser which is right in front of the radiator. There will be an electric fan that should be running when the AC is turned on. If it's not running, there won't be any air flow at low speeds and that will prevent the condenser from giving up its heat to the surrounding air. When the refrigerant stays hot, it can't absorb any more heat in the dash where it needs to start out cold.

More than likely that is the issue. I would suggest getting access to it and make sure it is turning the correct direction. A lot of times these gears strip out and they are moving but not to the correct location which doesn't give you the proper temperature.

Let me know if you have questions but I would replace this and then retest.