Intuition needs to be exercised and developed like any other aspect of training.
When we spend too much time breaking down techniques, analyzing details etc., a partial atrophy of intuitiveness can take place. I think technique is a tool of intuition, not the other way around (or at least it's equal).
In this way, perhaps, no mind can be looked upon as a link to intuitive mind. An open gate to the flow of emotive power; an over-riding of gut feeling over the analytical.
But how is it practiced? Perhaps just by listening to it on a regular basis. Not just in a martial arts perspective, but in daily life situations. By quieting the part of the brain that keeps nagging you with too much data regarding outcome and probability. Intuition, tied to instinct, can save you from hesitation. And hesitation in daily life can be as damaging as hesitation in self-defense.
Of course, there is time for intellect. No one should argue this fact. It's just that most of us practice this on a regular basis, while the other aspects often get silenced by the voice of "reason."