There is no air flow when the light goes out for extended time.
I suspect the clicking you can hear is the blower motor relay switching off which will stop the air flow. I think that relay also supplies power to the AC control panel so that's maybe why the AC is switching off too. It's difficult to diagnose the fault when it's only happening intermittently but if it's happening regularly you could try a bypass test on the blower relay to see if that cures the problem. It's not a fix but it will at least confirm where in the system the fault lies.