I often think about this, and the result is more questions, which if answered experimentally, might tell us a lot more about how 'consciousness works in the brain'
1)How long is 'now'. When you say the word 'hello', as you utter out 'o', is 'he' already a memory like the sentence uttered just before? (it seems to me not.. that 'now' is about 1/2 a second, and other things are in the past, and no longer consciously connected'. Similarly, a series of clicks (ie. via a computer) produced on a speaker, as they become more rapid, appears to become a 'tone' around 1/2 a second or quarter of a second or so...entering 'now'. It is as if, consciousness, has a 4th dimension (time) aspect to it, and to have consciousness, you need to span time a bit (in addition to the 3 physical dimensions of your brain).
Same goes for seeing a 'running man' on the road. It looks like movement, because what you saw a moment before, still seems like now, so a leg has a direction (forwards, backwards), as you see it move, remembering just the frame before.
2)What is red? What would need to be changed in your brain for anything in your field of view seen as red to appear as blue? Researching this, would tell us again, how the physical connects to the conscious. Then, what needs to be altered in brain memory (ie. physically), for a red box, to be recalled as a blue box. once we knew how to do this, we would be a long way to again understanding the connection to consciousness.
3)quantum mechanics (which is a principle widely believed that our brains operate under), talk about spooky action at a distance, and other interesting effects. Is it possible that quantum effects could also allow our brains to span processing across time? (even if it is just a second). Ie, again, when you hear the word hello, as you are hearing 'o', you are still aware of the letter h, not by recalling into memory, but your brain when it hears 'o', is still connected to the brain that heard 'h', a moment before (so processing is in 4D, not 3d). If brains could do this, it would be immensely powerful processingwise, and 'consciousness' may be just a side effect of that 4d processing.
My feeling is that consciousness is somehow related to being able to span time. We know brains are 3D. But maybe they are 'wide' in the 4th diminsion as well, which is why 'now' seems to take a large dicrete amount of time.
Just my thoughts, but trying to answer the above questions experimentally, I think would lead us a lot closer to what 'consciousness' is and how it connects to the physical brain.