But here's the problem. According to your stated criteria, two individuals could undergo identical soft striking training and achieve similar results. But suppose one student credits his skills to perfect, relaxed technique and the normal laws of physics and physiology, while the second student, being of a more "mystic" inclination, attributes his abilities to qi and fa-jing. Would you say that the first student is an "external stylist" and the second is an "internal stylist"?
You are starting from a false assumption, since Fa Jin and Qi are just chinese words for real world experiences that entirely obey the normal laws of physics and physiology.
It is true that some people associate these words, in particular the phrase 'energy' which is commonly used in their translation, for some kind of magical bullsh17, but that doesn't mean that these terms don't have a practical and pragmatic value.
So if, as you say, someone "attributes his abilities to qi and fa-jing" and correctly understands the meaning of these words (even if they are blended with mysticism) then they are still an internal stylist.
Nei jia (internal arts) in general and Tai Chi in particular rely exclusively upon the development of relaxed natural structure, having found that this structure is the optimal way to absorb, redirect, store and emit pressure (i'm deliberately translating the chinese word 'jing' as pressure so as to avoid the use of the term 'energy' and hence all the baggage that carries).
As humans our bodies are similar, as are the sensations that signal the correct execution of a technique, and while some elements of this are visible, demonstrable and explainable in terms of body mechanics, other parts are hidden within the structure, made visible only by the effect they have on the person who is on the receiving end of it.
Hence in developing this all important structure and learning to guide, store and emit pressure the student relies largely on their own internal sensations as a guide. These sensations (and the abstracted 'something' that seems to be mobilised and directed through the structure in practise) are typically lumped together under the umbrella term of 'Qi', a word that is also used for many other purposes, most of them mystical.
Emitting this stored pressure in a sudden and explosive fashion is called Fa Jin.
This is not so far fetched an argument as it may sound. There was an individual who used to post a lot around here. He insisted that his Wing Chun was an internal style because he did chi-gung exercises, and attributed his skill to internal power. Nothing that Xue or any of the other well informed folks around here could say would dissuade him. Now he has left us, "seeking tranquility". Would you accept his argument?
There are definately elements of the internal about Wing Tsun, especially in those practitioners who have refined their art beyond the reliance on muscular force and speed. Plus some (but by no means all), Qi Gung exercises are designed to develop internal awareness and through this nei jing (internal power - pretty much what I've been describing previously).
As such I cannot dismiss his claims as impossible, though since mystical imagination and misunderstanding of the basics is rife in the martial arts world it's highly likely that he was just deluding himself.