When you phrase it like "believe in intuition" that sort of... Comes across uncomfortably. Evidence supports its existence.
If you ever try programming something, you'll see how powerful intuition is. Breaking something down into a perfectly logical system is difficult (revealing quite a bit about intuition). From experience, I can tell you that coding bots to shoot each other is not as simple as just telling the bots to point and shoot. Bots, as we know them today, are stupid because they have no intuition.
Another great example I think is catching a ball. Somehow we manage to ignore the complex physics problem and just catch the ball.
Also, I'm not sure if you've ever heard of the term "flow" before. It's a concept by Mihaly Csikszentmihalyi. He describes it basically as a state where we lose self-awareness and sort of just do things. Generally, we experience flow whenever an activity demands all of our attention (when the challenge perfectly meets our level of skill). (I think it occurs a lot while playing video games.) Through this experience we are able to better ourselves, raise ourselves to higher levels of skill, and generally just do things better. I'm not sure I fully understand the concept, but I think that may be intuition there seeing as how the decisions are not being made by any kind of conscious rationale.
Anyway, the fact that you get intuitive thoughts and then disregard them suggests to me that you are an N, as I never get any intuitive thoughts myself.