In the Martial Arts we deal quite a bit with inuition, in the Japanese systems they call it "Haragei" ( art of the belly or Gut) and in other systems like the Chinese ones and the Indian ones, it is developed, like in the Japanese and Korean ones, to a high degree in some systems and less so in others.
It CAN be mystical, but typically, it is more martial though to many westerns the mystical part is hard to "not see", they are conditioned to see it as such.
Of course we can never discount the cultural influences also.
Intuition is great and is a very usefull tool, when coupled with reason AND experience.
A pianist practices daily a rigorous conditioning of the connection between the motor skills and the perceptive skills (sight reading of the notes).
At some point the active will to play (fingers on keys) what one sees (notes on the staff) is LEARNED and passes from CONSCIOUS knowledge to
MEMORY.
The piano piece can now be performed without concentrating on the "how".
We do not say the pianist is playing Chopin's Polonaise by "intuition". We simply say he has skill and talent and experience.
That is why I'm "calling out" as it were the term: INTUITION.
It is doing double-duty.
We err when we try to use the word this way: mystical and practical.
What the pianist does when he plays a learned etude is call upon something acquired by dilligence and an active mind which has BECOME non-conscious and available. Nothing mystical is involved.
Unless and untill we SEPARATE from our mind the two contrary definitions (mystical from practical) we are destroying our understanding rather than employing it. Anti-Concepts vitiate consciousness.
Remember this: when you don't understand what you are thinking you are at the mercy of others who can manipulate your BELIEF for their own interests.
Relying on BELIEF rather than understanding makes us susceptible to influence.