I could not find a good word expressing "a feeling approaching the solution of the problem". On the other hand, the opposite "a feeling away from the solution of the problem" has a good word "IWAKAN"(discomfort).

That is feeling of "something is wrong, although ​I can not say what is wrong"

Programmers often express the feeling that there is something wrong with the source code as "code smells". *34

This is another way of saying, "I can't really say what's wrong, but the source code is in a kind of bad state."

This bad feeling is expressed by the physical sensation of "smell."

I'm sure you have all experienced this kind of "IWAKAN" feeling. However, because you have not been able to verbalize why it is wrong, you tend to ignore the feeling. However, it is rather the opposite. The feeling of discomfort is an important sign that there is something which need to be verbalized. If it is not yet verbalized, it will be in the future.

*34: For example, it is mentioned in Martin Fowler's "Refactoring".