It seems to me that pretty nearly every idea is the result of unconscious processing of data which surfaces during some sort of "daydream". "Eureka!" is an example, so was Newton and the apple, Feynman with spin.

There are the Walter Mitty "pocketa pocketa" daydreams, the rehashing of discussions with a boss, the more topical daydreams.

Then there are the problems one sends down into the unconscious, where they are processed for sometimes days and weeks before the answer surfaces as "intuition". That can be controlled by meditation, which is clearing the mind of words. One can ask one's sub-conscious for an answer to a specific situation in a day or two and then forget about it, and the answer will appear in a day or two.

More goes on in the mind than we can know (odd, isn't it?) and it's a willing tool.