The first thing you have to clarify if you want to type Jung is: under whose system? Do you mean the result Jung would have gotten if he'd taken the MBTI or a (possibly different) type based on the cognitive functions? And if you mean the latter, are you talking about Jung's conception of the functions or the substantially different (in many respects) function descriptions/model that modern theorists like Thomson, Berens and Nardi use?
Myers acknowledged that most Jung scholars believed that Jung thought the auxiliary function would have the same attitude as the dominant function, not the opposite attitude — and you can (in case you're interested) read a lot more about that in this two-post extravaganza. I think Myers was wrong — and the majority of Jung scholars were right — although it wasn't a very significant mistake from Myers' perspective since, although she gave the functions quite a lot of lip service in the first half of Gifts Differing, she then essentially left them behind in favor of the dichotomies.
I think the interpretation that's most consistent with Psychological Types as a whole is that Jung's function model for a Ti-dom with an N auxiliary (for example) was really Ti-Ni-Se-Fe — with Ne being a Ti-dom's default, unconscious form of N and Ni being the form that N would take to the extent that the Ti-dom differentiated it and brought it into conscious, directed use as the auxiliary function.
It's clear that Jung viewed himself as a "rational type" (i.e., J-dom) at the time he wrote Psychological Types (because he told us that), and I really don't think there's any doubt that means Jung viewed himself as a Ti-dom at that time. And, judging by the way he described rational types (and, to a lesser extent, introverts), I suspect that the fact that he viewed himself as a Ji-dom means he would have tested as an MBTI J if he'd ever taken the MBTI. If you read through Psychological Types looking for two-kinds-of-people-in-the-world descriptions that seem to line up reasonably well with the MBTI J/P dimension, you'll mostly find them in Jung's descriptions of the J-doms and P-doms. Jung said P-doms "find fulfilment in ... the flux of events" and are "attuned to the absolutely contingent," while J-doms seek to "coerce the untidiness and fortuitousness of life into a definite pattern." He said a J-dom tends to view a P-dom as "a hodge-podge of accidentals," while a P-dom "ripostes with an equally contemptuous opinion of his opposite number: he sees him as something only half alive, whose sole aim is to fasten the fetters of reason on everything living and strangle it with judgments."
Here's a link to Part 3 of an interview done with John Freeman when Jung (born in 1875) was 84. Forward to around 8:40 and you can watch this exchange:
JF: Have you concluded what psychological type you are yourself?
Jung: (chuckling) Naturally I have devoted a great deal of attention to that painful question, you know.
JF: And reached a conclusion?
Jung: Well, you see, the type is nothing static. It changes in the course of life. But I most certainly was characterized by thinking. I overthought from early childhood on. And I had a great deal of intuition, too. And I had definite difficulty with feeling. And my relation to reality was not particularly brilliant. I was often at variance with the reality of things. Now that gives you all the necessary data for the diagnosis.
So Jung was clear about his N and T preferences, and was clearly introverted (as I understand it), but sheepishly confessed that he'd found his own type to be a "painful question," which suggests to me that, at least during some phase of his life, he must have wrestled with the issue of whether he was a Ti-dom with an N-aux or an Ni-dom with a T-aux — comparable (you could argue) to the confusion of all those forumites who wonder if they're INTJ or INTP.
Because of the way he describes his preferences in the interview, he seems to be pointing to Ti-dom with N-aux, and that's the way he's most commonly typed. But if you take a look at this page, you'll see Vicky Jo's "news flash" to the effect that Jung reportedly told Stephen Abrams (a Jung scholar) in 1959 that he was an "introverted intuitive." And, in this follow-up report, Vicki Jo quotes Marie-Louise von Franz (one of Jung's prize pupils) declaring that Jung was an N-dom.
As a side note, I think it's pretty clear Jung was Limbic (neurotic) on the Big Five dimension that doesn't have a corresponding MBTI dimension, and that he considered at least some of his neurotic characteristics part of introversion. He also viewed much of what most MBTI theorists today would tend to label the abstract/concrete component of N/S as part of I/E. So, when Jung describes "introverts" in Psychological Types, his descriptions tend to be better matches for neurotic INs than for introverts in general.
Finally, on T/F... I think T/F's the messiest of the four MBTI dimensions, and arguably the one that's the most poorly captured in modern MBTI sources — and I think there's a strong case to be made that Jung didn't have all that good a grasp on how an F preference would tend to manifest itself in, say, a male (in particular) INFJ. It's not uncommon to read that Jung was an INFJ, and people making that claim often point to his mystical bent, among other characteristics more typically associated with NFs than NTs. I view INFJ as the second-most-likely type for Jung, and I'm also a believer — consistent, as I understand it, with quite a lot of MBTI and (especially) Big Five data — that it's possible to be sufficiently middle-ish on most, if not all, of the MBTI dimensions that an "x" is at least arguably the best label to use. So I also think it's possible that Jung was effectively an INxJ.
If forced to choose, though, I'd choose INTJ. And, as already explained, I think that typing is consistent, rather than inconsistent, with Jung's view of himself as a Ti-dom.