I think something can be said about intuition - mostly indirect and negative-definition; but it is useful to know some-things about intuition, given that it seems to be a mode of though characteristic of creative geniuses (when they are being creative geniuses).
We could approach intuition by stating that intuition is the mode of thought of the private soul/ the real self/ inner consciousness - that is to say the most profound, the most secret, fundamental mode of thought.
Intuition can be contrasting with two (lower, subordinated) modes of thinking passions versus reason; the body v the brain; gut-feelings v head-knowledge; instinct v logic.
These two modes are not absolutely distinct, but I think can usefully be distinguished.
The soul is usually (as it were) hidden beneath the busy activities of the mind and body, bombarded by perceptual data, sensory inputs, and unaware of itself. The soul is 'fed' by the mind and body.
But when these inputs are stopped, then the soul can (as it were) distinguish itself - and these inputs are stopped in sleep, in trance states - when the inner activities are insulated and isolated.
So, what is the mode of intuition? It is not by instinct or by logic - but by something of both and more. Therefore, intuition is a mode of thinking which simultaneously uses emotion and logic but is a context of (for example) motivation, purpose, meaning, relationships etc.
The result of intuition is therefore an evaluation which is uniquely convincing because it is validated by the full range of positive responses.
By contrast, even we use only (for example) logic, or only emotions, to evaluate something; then the evaluation will be incomplete, and evaluation in one sub-mode may be contradicted by evaluation in another sub-mode - as when logic and emotions reach different conclusions, point in different directions.
Only the evaluations of intuition are fully satisfying, fully convincing, and harmonious. Only the evaluations of intuition mobilize the whole range of thought modes.
This intuition is the most powerful mode of thought, and the only mode of thought capable of mobilizing the fullest motivation. This is why intuition is necessary to the highest levels of creativity, to the greatest attainments of genius.