Nick, I think you have answered your self with your original question. Intuition, perception and insight. I would like to think (definitely hope!) that this can be trained and improved.
I had the joy of watching Pink Floyds Saxophonist, Dick Parry play recently. I was entirely mesmerised by his ability that was without a doubt sheer genious. He played in a trance like state, body completely quivvering as waves of whatever you would like to call was flowing through him, being translated and converted by him into sound. To say the least, he looked like he was a world away. He had completly immersed himself in the void, but never became lost in it.
Perhaps there's no real earthly translation or map for that state...at least I think there are limitless, and ever changing variabes involved in it. Perhaps we just mould it in time to work for us. This has to get better with experience/age providing we're constantly striving to do so. Constantly asking our selves how we can do it better next time. More of a gradual trickle of knowledge.
I'm not sure we can discount what gets us there in the first place for I feel it's in identifying it that could take that state further. I would, as I'm sure everyone here would be very interested in what you thought about the factors that "combine to get one there,e.g.motivation,desire,and the factors that conspire to keep one grounded,e.g. fear,distraction".
Previsualising the outcome...Perceiving the moment...moulding the energy available...balancing empathy with the subject, and your own voice...PLUS willing to diverge from the intended path of concept to allow what magic the moment has to deliver. Translating it technically and graphicly, all whilst patting our head and rubbing our stomach in circles. Easy surely...? :) I'd like to think that our ability to do this becomes better with age/experience.
As others have said above though....BIG question. I remember reading in DaVinci's note books that even he wondered how man could go any further in such "advanced technological times"...he later went on to invent to the Hellicoptor amongst other things.
Thanks for the discussion.