gut feelings have a huge place in discovery science (what these scientists are doing). It can lead you in directions that rational cannot. For example, Kekule's dream of ouroborus: " He said that he had discovered the ring shape of the benzene molecule after having a reverie or day-dream of a snake seizing its own tail (this is an ancient symbol known as the ouroboros).[14]"

I've been privileged to know a lot of world-class scientists, and many of them have told me their careers and their best ideas came from gut feelings. Of course, they had to apply skepticism to the experimental results of their gut feeling experiments.

Exactly. Gut feeling is another word for intuition. Such background cognition is a great tool in science and has been found in use by a lot of top scientists and thinkers. Training it by broadening your knowledge and then using skepticism and other science tools to focus your thinking is a great way for finding stuff out.