Perhaps the common factor here is Introverted Intuition which is the ISTP's tertiary function?
I see why you would believe this, however Ni is almost non-existent for ISTP at the teritary level. It would make for something totally different than being in the dominant function. I attempted to locate a good description, however MBTI seems to still be lacking on providing good information when it comes to teritary. I attempted to paste an example from Lenore Thomson's Wiki site, but the description was bit over the top.
INTJs and ISTPs have an intense need to apply theories for different reasons.
INTJs because their judgment is extroverted and ISTPs mostly due to the Se. Albeit the tertiary Ni is also a factor. Ni demands that its visions be made a reality and Fe, being the inferior function tends not to have a voice of its own, so it just cheers the Ni on. But again ISTPs need practical applications because of their Se, which is the hallmark of 'SPness'.
Your example for why INTJ has a need seems to be lacking. Again, I attempted to locate a good description of how Te works as an auxiliary function, however Lenore Thomson does not even offer one, which is surprising since she is an INTJ. Nevertheless, Linda V. Berens and Dario Nardi gives some good insight as to why ISTP closely resembles INTJ (and to some extent INTP):
ISTPs have a Chart-the-Course Interaction Style, which goes with a desire to enter a situation with some sort of course of action in mind. It doesn’t have to be a detailed plan and ISTPs often seem planful as they analyze a situation in anticipation of what is likely to happen. ISTPs and INTJs share this Interaction Style and so would look alike in that way.
The Chart-the-Course style often seems like the Strategic intelligence that is an important aspect of the Rational temperament pattern and ISTPs often relate to the description of the Rational temperament over the Artisan temperament. This is especially true when the Artisan description focuses too much on freedom and spontaneity.
There are some tell-tale differences at the temperament level:
Differentiating Artisan versus Rational is key. Artisan desire for skillful performance often leads ISTPs to identify with the Rational’s core need for competence. In presenting the two temperaments, it helps to contrast the difference between skillful performance as a value and competence as a core need. For the Artisan skill often comes from the drive to action and they hate being clumsy or awkward. They get involved in an activity, get caught up in the pure joy of doing, and thus become skilled. Rationals need to feel competent and often want a measure of competence before they even do something. To practice or “do” means failure and that often can strike at the core need.
Another difference would be in how the two communicate. I was recently accused of not communicating, on this forum, like a SP, instead sounding more intuitive:
It helps to listen for the concrete language of the ISTP, which often creates a picture in the listener’s mind. Such language is likely to be full of specific examples and stories. INTP and INTJ language tends to reference abstract concepts with a focus on precision. ISTPs often get at the essence of something rather succinctly, whereas, INTPs and INTJ go into more depth.
Since ITPs share the same dominant function, ISTPs think more like INTPs, than INTJs. ISTPs analyze; INTJs conceptualize:
ISTPs and INTPs have the same Leading Role process (dominant) of introverted Thinking and are likely to approach situations with an analytical perspective and like to know the principles of how things work. The difference shows up in their Supporting Role processes (auxiliary). An INTP described his preferred work style as exploring problems and sub-problems (Ne), while his ISTP colleague described a tactical trouble shooting approach with a focus on getting the task done (Se).
I don't know, it's too close to call whether I am INTJ or ISTP, but still leaning toward ISTP. Berens/Nardi does provide a brief example of the Ni for ISTP:
Also, ISTP’s frequently engage their Relief Role process (tertiary) of introverted iNtuiting and enjoy looking at whole systems and patterns and getting a sense of what will happen in the future.
However, without further understanding I am unsure how that role plays out.