You can have Ne as first (strongest) and still come out as INTP (like me). That would depend on the relative strengths of the other functions.
So you're saying it should be Ti-Ne-Ni-Te-Fi-Se-Si-Fe or Ti-Ne-Ni-Fi-Te-Se-Si-Fe. That does seem to be close to what many are getting.Si is the complement of Ne.
I find it difficult to understand people can be unconcerned about balance. There is no pattern without a balance.
And as you say, the pattern can be seen in the test results. If Ti is the first function, it follows Fe is at the other end of the line and Te and Fi complement each other in the middle as the 4th and the 5th. If Ne is the second function, it follows Si is close the other end the 7th, and Ni and Se complement each other near the middle as the third and the sixth.
This is the medial line, it has a sway, it is not rigid. The middle functions, the 4th and the 5th, change places frequently. The more you move towards the edge, the more it would disturb the balance.
If Si is the third, then we have to look for Ne, and Ni and Se. If the P functions do not have a pattern, it is not likely the J functions can have one.
All the possibe patterns are related, and their number is limited. The choices are easy to see. Ne and Si, as second and third, simply do not thyme in any of these.
But with both attitudes of the perception functions next to each other like that, wouldn't that create unbalance? In one case, the primary functions are T-N-N-T. I guess that would go along with the ultimate NT preference, but still, in the original Jungian conception, (dealing with only the four), there was supposed to be a balanced primary use of all four processes (in one attitude or the other). It doesn't seem likely that all forms of Sensing are ego-dystonic to us. (Remember, Jung's concept was about ego-consciousness, hence we must be conscious to one form of all four processes).
It seems to make sense the way John has it. You have alternation of J-P-P-J; and attitudes e-i-e-i; and then the same J/P order, but with hte attitudes reversed for the shadows. The CP test would to me indicate that some functions are either overdeveloped, or underdeveloped (and of course, also the possibility that people are misunderstanding questions. I thought I was very good at Fi stuff, and initially came out as INFP, but then had to rethink what stuff like "staying true to what's important for you" meant. And the site says that it's NTP's that get the most hung up on the way questions are worded).
The book "Understanding Yourself...The Personality Type Code" breaks each type into the eight functions, and how they work out, in the ideal preference order. I find it pretty accurate, even for the functions that are out of order.I have nothing against what John and Linda say, as such. And I know they are not into function order. Perhaps it would be better to leave it out, entirely. For them.
Thanks for mentioning the archetypal roles, too. I shall look into them.