I think Ni is how I make crazy, yet almost invariably correct, intuitive leaps. I believe this coupled with Te is how I see through things, too. I'm knows for this mysterious ability to see into black boxes, tell people how they work (correctly), and tell people that have intimate knowledge of their inner workings what's wrong inside of them. It's some kind of pattern-matching/forming system - everything has a pattern and it's just a matter of finding it.
"Do you see the method that handles X?" ... "There's a problem in the loop there that manipulates Y.", "I see it", "Now, move it to Z.", "Done", "It'll work right now. Thanks."
Don't ask me how this works, it's magic. It's like how I solve problems or select from a group of solutions, only that I can usually come up with many rational reasons one is better than the others. If an INTP totally trusts you, they'll follow your choices from their list of well-thought-out ideas/solutions, even if you're really just giving assorted reasons why one is better than another and the only reason you advocate one is because it just stands out as the best to you, so you actually manipulated the values of different positives/negatives to get the choice accepted. It's not perfectly rational - it's magic. Some kind of highly flexible pattern matching coupled with an ability to approach from seemingly-random angles, which coupled with my Te allows me to distill them down to the best solution. I can also originate ideas, but then I might have realized in retrospect that I missed some possibilities that would have been better, so I either re-implement something right or leave it for later if it's sufficient and doesn't decrease the result quality of future choices.
It also allows me to see outcomes of choices/actions, even if they're vague, because certain ones are better than others. It probably makes us the best strategy game players (ex: chess) and is the reason we optimize high-payoff strategies for every game (ex: scrabble, poker). We do everything based on intuitive payoff values, so our route is controlled by these payoff value choices.
I expect that one of the weirder/scarier things to an SJs would be watching an INTJ and INFJ that are really close discussing things that are totally illegal and immoral. The INTJ will totally ignore morality and support the INFJ's most evil fantasies, coming up with ways to do them, telling them the best way to do it, get away with it, etc. One of those powerful teams that could be for good or evil mattering on how the wind blows. (Like INTJs and INTPs, except it'll usually be for some positive purpose, but that purpose could theoretically be anything.) I'll just say that some conversations I've had with the most loving INFJs, particularly out of the context of the relationship, would probably scare most people.
The noise in my head when I'm going to sleep is very weird. I can have "conversations" with virtual patterns of people. Sometimes I'll have online chats with people in these twilight dreams.