I love the discussions on the 'make up' of a good player, I am writing this as the parent of a 10 year old who I am trying to teach the valuable life lessons of this wonderful game. I guess you know IT when you see IT. Here's my contribution that I believe removes the age factor from the conversation.
You cannot buy IT or be given IT. There is no shortcut. Some will never get IT because they are unable or unwilling to put in the work necessary to attain IT. Some are unable to understand the difficult process to get IT. You have to work very hard and fail over and over before you earn IT. Many quit or give up when they fail in their 1st attempts in pursuit of IT.The one's who truly earn IT are the one's that you love to watch. They look different in taking the field, fielding a ground ball, catching a flyball, swinging the bat. They're the one's that have IT and have truly EARNED IT. The intangible that separates the good from the very good is CONFIDENCE. Confidence in one's ability, in their understanding of the game or the situation. IT is very powerful, but as powerful as IT is, IT is also very delicate. IT can be taken away by a coach, a parent, a teammate. When you see someone who has IT, tread lightly. The road travelled to attain IT can be a very long and difficult one and repairing or searching for IT can be more difficult the 2nd time around.
I write this as a Steve Springer fan and believe that this is what sets someone like Pedroia a part from others. He has ability and tools, OBVIOUSLY, but his 6th tool is the confidence he has in himself and in his ability. It doesn't waver or fail him because he has built his confidence to the point where it cannot be taken away from him. He doesn't question himself or the results.