This chain of thought was spurred when I was thinking of why INTJs are not associated with the "Spacy/Dreamy" qualities that Jung associated with the Ni dominants, the traits often found in the archetypal INFJ for example.
I think functions are inherently masculine or feminine, not developed to be such a way as some other theories suggest.
This comes from the idea that introversion is inherently more feminine than extroversion. Sensing is more masculine than intuition. Feeling is more feminine than thinking, and judging functions are more masculine than perceiving ones, or so I am at least proposing theoretically.
Thus Extroversion is a masculine trait while introversion is a feminine one. Sensation is a masculine trait while intuition is a feminine one. Thinking is a masculine trait while feeling is a feminine one.
Introverted intuition = Feminine/Feminine
Introverted sensing = Feminine/Masculine
Introverted feeling = Feminine/Feminine
Introverted thinking = Feminine/Masculine
Extroverted intuition = Masculine/Feminine
Extroverted sensing = Masculine/Masculine
Extroverted feeling = Masculine/Feminine
Extroverted thinking = Masculine/Masculine
Now, as Briggs notes in Gifts Differing, "The introverted types can often be mistaken for their extroverted counterparts when presenting the auxiliary function."
When you think about this in relation to the idea of the sexual orientations of the functions, then you come to some interesting conclusions, specifically within the introverted types.
Let's look at the introverted irrationals, the IJs.
The INTJ leads with Ni, a feminine/feminine function. So does the INFJ though. The difference between them though is that the INTJ has Te as its auxiliary function, a Masculine/Masculine function, while INFJs have Fe, a masculine/feminine one.
This means that despite the inner world being of a Yin nature, feminine/soft, in the INTJ, the outer world is of an entirely Yang one. When looking at the INFJ their inner world is of the same Yin nature. The difference though is that their outer one is of a balanced masculine/feminine one, due to the nature of Fe.
This means that that INTJs are of a significantly more masculine nature right? Well, no, because the temperament of a type is not even when looking at the first two functions. The auxiliary function exists only to serve its lord, the dominant function, which makes up a large majority of the conscious self. What it does do though is lead to a slight inclination towards the traits of that orientation, a tilt in the compass away from the true North of the femininity of Ni, where INFJs have less of this influence.
Let's contrast INTPs and ISTPs in the same nature. When we think of these two types we often imagine the archetypes of the scientist for the INTP and something akin to the engineer for the ISTP. Which of these two inherently sounds more masculine?
Introverted thinking is a feminine/masculine function, so it is relatively balanced, specifically as a dominant function, which leads to a greater balance of the two than even in the Ni or Fi dominant types which hold to complete yin nature.
What differentiates the INTP and the ISTP is again the auxiliary function, which is most often presented to the world as it is extroverted. The INTP has Ne, while the ISTP has Se. Ne is a masculine/feminine function while Se on the other hand is a masculine/masculine one. The outer presentation of the ISTP is of an entirely masculine nature, while the outer presentation of the INTP is of a relatively balanced nature, aligning with the dominant function.
This can even be seen in the extroverted types with how the introverted function supporting it might influence this energy.
Look at the ESTP vs the ESFP. A double masculine leading function that is supported by either a feminine/masculine one (Ti) or a feminine/feminine one (Fi).
Thus the ESTP is often associated with the archetypes of the athlete, the fighter, etc., while the ESFP is associated with the musician, the artist, etc.
A further step introducing the inherent M/F of perceiving vs judging could also be theoretically added, but I think this attribute does not hold the same significance and makes differentiation harder. For example, Ni is Introverted (F) Intuitive (F) Perceiving (F) function - so FFF. While introverted sensing is an Introverted (F) Sensing (M) Perceiving function - so FMF. I personally think it is better to approach this topic via two layered M/F via the attitude (I/E) and gender expression of the nature of the function (T/F/N/S). That said, the third gender expression letter, in theory, should not be entirely ignored.
All in all, I think that these things matter in the presentation of types and could even have impacts on the expression of traits within people of the same type of different gender or gender preferences in relation to the gender norms of their culture/environment.