For quite a long time, I have been about to write about this. Now I finally did it
It's about the dualism caused by having no preference for J/P. I, for one, am an INTx and because of that, I often feel like I had two persons inside of me that have different motivations and no ability to co-appear. It's not about schizophrenia
In practice, I kind of have to modes I can be in and it's somewhat consuming to find the mode too often. In INTP mode, my main motivation is to understand, and in INTJ mode, my main motivation is to accomplish. Depending on the situation I am in, my actions may depend strongly on the mode I am in.
There has, for example, been cases that I have met a girl in INTJ mode, found her attractive and successfully approached her, just to a bit later find out that in addition to that girl being attractive, there has been something in that girl that has awakened the interest of my INTP side to learn or understand something new. Unfortunately, I may have at least once lost a girl because of my INTP side taking over at wrong moment and turning me more interested in something else than the girl herself.
The same goes for countless other situation that have varied based on their seriousness. The common fact for all of them is that I have had to choose whether I want to learn/understand or accomplish/gain and that I usually have to base that decision on rather limited information. Or, as in that girl's case, I may not be able to control to selection at all.
According to my reasoning, one can't use both introverted and extroverted side of a function (S, N, T or F) at the same time. They would contradict in a way that is not possible. For example, Ne is about observing patterns in the world around and Ni is about finding connections between various things that you have already discovered and what you are discovering. Ni needs it's time to take information in where as Ne works more or less in real time. Whatever Ne notices, it can't become part of the Ni information storage immediately, and letting Ni to work out something kind of prevents concentrating on the world around which would be required by Ne.
Assuming equal development of cognitive functions, having no preference for P/J means that one should have at least one or two out of S, N, T and F well developed regardless of their attitudes. In my case of being INTx or INTJ/INTP or NiTe/TiNe, that would be true for T and N and cognitive function test actually proves that.
I'd be very interested in hearing any comments or experiences.