I'm a pilot for a living and I have been flying for over 20 years. While I'm not a doctor, something I wanted to add to this discussion was the experiences I have had in altitude chambers, where we were exposed to oxygen deprevation and hypoxia.
They bring the altitude chamber to 25,000, 30,000, and/or 35,000 feet, depending on the training (I've done all 3) and individuals take turns removing their oxygen masks and trying to function at those altitudes.
One student, a pilot training candidate, took his off at 35,000.
Within approximately 20 seconds, his lips and fingernails were blue (cyanosis), his speech was slurred, and he was having difficulty thinking (we're asked to perform simple tasks, like writing our names, etc).
By 30 seconds, he was no longer responding; however, his eyes were opened and he was looking around. He didn't fall over or pass out. This is normal for hypoxia, though it differs from how Hollywood and the media portray it.
He was told he was "going to die" if he "didn't put his mask on".
After repeated attempts, finally the instructor told the student next to him to put the incapacitated student's mask back on for him.
Before he could do that, one of the other students yelled, "EJECT, EJECT, EJECT!" The hypoxic student immediately started reaching for the ejection handles.
As soon as his mask was back on, the student returned to trying to write his name on the paper and was unaware of what happened inbetween, thus he had no memory of being told he was going to die or that he tried to eject.
I think the lesson here is that there are reflexive responses and there are conscious responses.
In the case of beheading, yelling the victim's name and having him look towards you definately indicates brain activity on some levels, but the response may be purely reflexive, and does not necessarily indicate that the victim is conscious and aware.