The Eureka Moment is rather like trying to remember something that "you know that you know", but you can't find it in your memory. Much of brain activity goes on outside of our conscious attention. When we direct and "push" our thinking is the direction that we believe the answer lies we make prevent the appropriate brain state from emerging. If we just put in the information that we know and then let the brain do its own natural interactive pattern matching, it will tend to gravitate to the point where "awareness" is. In terms of a holographic memory approach (which my research favors), The various interference patterns created by incoming sensory information, our present state of consciousness, and the additional interference patterns which get triggered when words, ideas, visualizations, etc. (which are contained in those somewhat random patterns) will sync and converge. The electromagnetic energy patterns (or interference patterns) will seek to achieve energy conservation, by joining and syncing with other similar patterns rather than fighting them (which we do when we think we know where we are going and are in fact going in the wrong mental direction). This just adds to the general noise in the brain. "Letting go" basically allows the brain to operate by itself and it can find what it needs.