I'll propose an answer to the question. My super-abstract hypothesis is:
The brain has two halves, each circulating data somewhat independently of the other, each maintaining a continuously updated "model" of both physical and abstract environments. Each half is also monitoring the activity in the other half through the corpus callosum. This is sort of like the TV "picture in picture" feature. Because there are two sides, each monitoring the other, we get an effect not-unlike standing between two mirrors facing each other. Looking at one side gives us a picture somewhat like when the TV camera is pointed at the monitor, showing a TV containing a TV containing a TV containing a TV, etc.
In the days of the bicameral mind (Julian Jaynes), culturally imposed "software implementation" (see the Sapir-Whorf hypothesis) did not "superimpose" the two sides well. Operation tended to switch from one side to the other, so that individuals spoke about themselves in the third person, and received intra-brain-half communications as the appearance of external manifestations. With the "breakdown of the bicameral mind", the two sides achieved a greater synchronization allowing us to experience the external world as vivid "qualia" while the "picture in picture" gave us the sense of watching ourselves at the same time. So consciousness is a particular way of brain function that depends on hierarchical organization with dual processors that each monitor the other recursively with time sharing that implements two additional "virtual" processes (the synchronization effect) - a world monitor/responder and a self-monitor.
In very busy conditions the resources of the self-monitor are suppressed in order to support world monitoring and responding, so that a person can be "too busy to be aware of him or her self". Awareness of the world? - Yes. Memory of events to draw on? - Yes, Awareness of self at the time of busy activity? - No. The busy activity can, of course, be interrupted at any time to bring out the awareness of self.
May 17, 2006: Prof. Rafael Malach, Ilan Golberg and Michal Harel of the Weizmann Institute’s Neurobiology Department found a scientific means of addressing this question – by scanning the brains of volunteers performing various mental tasks. The results of their study, which were published recently in the journal Neuron, were unanticipated: When subjects were given outwardly-focused tasks that demanded their full attention, areas of the brain that relate to the self were not only inactive – they appeared to be vigorously suppressed.