That's interesting. I always contrasted myself with my INTP father because he is more methodical and precise, where I'm pretty straight-to-business and tend to experiment within reason. I think my ISTP brother falls in the middle. He's definitely methodical and precise too, but he also tends to be fairly practical whereas dad is heavy on the idealistic constraints. I'm all about just getting something to work and then letting the TPs figure out how to make it work best.
I think my steps would be something like:
1. Attempt to solve the problem intuitively on my own by tinkering, figure out main snare/s
2. Research subject starting with snare and expanding to holistic understanding
3. Apply understanding to tinkering
4. Repeat until solved.
* If no luck after reasonable attempts, or under time pressure, find someone better-versed in matter