The dramatic loss of blood pressure leads to shock, so even if the brain seems alert and responsive, it has no awareness of pain or often even what’s happening. As a child a friend of mine fell through a deck and one of the boards completely went through his leg. He was talking to us like normal and even trying to walk around while we were waiting for an ambulance, and after the fact he had no memory of the fall or of the time spent waiting. So, even if the brain remains active after the guillotine or firing squad, it’s highly unlikely that the person is actually aware even if they’re responding to stimuli.