Not necessarily the cockpit, but nearby. This is a somewhat ambiguous area. The APU is not approved for "unattended" operation, although this term is not clearly defined. It generally is taken to mean a crew member must be in or around the aircraft while the APU is running. They might be sitting in the cabin, loading bags in the baggage area, outside but only a few feet away to supervise fueling, etc. The main issue is that the APU has numerous safeguards to shut itself down in the event of a mechanical problem, but if it shuts down with all of the lights/avionics powered on, the main ship battery will only last for about ten minutes. If a crew member is not present to promptly shut down the avionics and lights after an APU failure, they'd be stranded with a dead APU and dead battery.
Thanks for the great videos. You also explain and simple to understand the systems; Excellent presentation... now I know what a professional is supposed to be Captain it will be possible that you can prepare some videos Citation 560XL will be very grateful Thank you very much in advance Robin Raphael Rivera-Pomales