Although it is very hard to isolate cognitive functions and describe them, I' m curious about your opinions about them.
My personal views are that Te is most of an hierarchy function which sorts and structure feelings, thoughts and objects.
So, Si - Te will sort sensations and objects, quantify time, Fi - Te will sort feelings and give them values, Ni - Te will sort ideas and plans, put them in the right sequence.
Ti is more like the philosopher of the mind. Interpreting thoughts, external impulses and feelings, choosing the right explanation for everything. So Ni-Ti and Ne-Ti will be like a strong future debate, the difference being that Ni will generate one thought into multiple ideas, while Ne will absorb multiple thoughts and put it in one perfect idea. (My view of this combination of function). In rest, Ti, is very hard to detect, Ti sometimes it will be identified as an Fi, yet it mostly deals with objective subjects. I don't know how it functions in the Mechanic and Doers personality, it' s like there isn't any mountain they can't climb, or there isn't a thing they can't sell, Ti with Se might be the competitive nature of man. Ti and Fe will find the right word for other people feelings, or Ti will block Fe and Fi. Ti and Si Fi used together is the anxious state of being.
XXFP
The problem with Fi-Te is that here Te is either in the tertiary or inferior position. In many people, especially younger people, it will be wholly unconscious or at least very suppressed. It may be possible that as people grow, Te plays some part in supporting their Fi, but Fi at least as a standalone function is still a judging function and still has its own capacity to quantify and measure things; just according to a different standard. Fi is the literal opposite of Te, so to suggest that Te supports Fi is perhaps a little wonky here.
It's like saying that in ENFJs, Ti supports Fe in making value judgments. It doesn't - Fe is its own system of values and ethics derived from an alternate perception of the world to Ti. In certain circumstances, the ego might prefer to use one or the other (and this is where your function order comes in) to decide various things, but whether it uses one to provide the other with logical data is, I guess, questionable. I don't personally know but I would strongly doubt it.
XXTJ
Where Te is
supporting another function in the auxiliary position, I agree that it can give a sense of empowerment to that particular function, whether it is Ni or Si. The desires of the way that the ego perceives the world through Ni and Si can be expressed by the use of Te if the psyche itself is sufficiently cohesive and developed. This is how INTJ gets a stereotype of Engineer and ISTJ a stereotype of a post office. Te gives a sense of order to the perceptions of the world that Ni and Si create.
Where Te is the dominant function, iin these types we observe the greatest preference to external order. The dominant method in which they view the world is through Te and Ni or Si give them a way in which the things they are ordering can be
interpreted; with IXTJs, the Te orders what is being interpreted; with EXTJ, the interpretations are applied to the order.
I like your comparison of Ni and Ne. It's very accurate and succinct, I think.
However it's perhaps a mistake to look at Ni and Ti. This only occurs in some types and the chances of the psyche observing and interpreting the world with these two functions of its view are probably scarce.
I cannot speak for ISTPs but for ESTPs, Ti fulfills the important function of judgment. It is wrong to say that Ti deals with objectivity because as an intraverted function, it is necessarily subjective. On the other hand, Ti does have a relation with objectivity. It is the case that while we observe the world primarily through objective facts, objective facts on their own are of no standalone value. I can look at a telephone and think "This is a telephone that does not work." This is what Se will do. However, to actually
do something about it, rather than make that simple observation in its totality, we need to be able to apply some form of judgment.
This is where our Ti kicks in. Internal frameworks of logic take the facts that Se is drawing from the external world and view them from a subjective view point. Ti aids Se in the ESTP in the same way that Te aids Ni in the INTJ.
In the INTJ, they will create their ideas from a subjective view. They will then use the objective Te to apply external frameworks of logic because Ni is not capable of this. This is why INTJs are stereotypically good at fixing things; they can collate all the information theyve received into one idea and then act on it with an objective capacity for logic.
With the ESTP you are looking at the world primarily through an irrational function, Se (P), like the INTJ does with Ni. But you are already receiving an objective view because the ESTP's primary function is Se, which is hella objective, perhaps the most objective. But to actually do something about it, you need to apply some form of rational view. That is where the Ti comes in. But unlike the INTJ, who's rational view is external and objective, the ESTP's is internal and subjective.
Does this help at all?