"Think nine times then play once but not the other way around."
But it's not "thinking" as such. It's more like you said: being present. A little bit like zen meditation. I find if I start thinking rationally, I lose it. It's listening attentively to every note and "being there".
My teacher pretty much describes this as hearing everything in perfect clarity in your inner ear, then willing it into being.
I took a lesson from a golf pro once. I hit a shot. He asked me to grade it from 1 to 10. After i did that, he had me grade my intent before the shot from 1 to 10. Well, the shot might have been a lucky 6, but the intent was a 1 that time. It was one of those zen moments. Focus, concentrate. On the other hand, I was at a lecture from a world famous trombone player. I won't use his name, but you've heard him a zillion times on studio recordings etc. Someone commented that his life can never be boring, he's always doing some different type of project. He replied, "well, yeah, but for 45 years I've started every single day with an hour of scales." He also said...........sigh...........blew my mind, but he said it..........he often practiced while watching soap operas on tv.