Nietzsche is hard to type because to me he's displaying behavior that would fit either INFJ of INTJ.
His Ni dom is unquestionable but I'm still on the fence with IN_J.
There are some aspects which to me seem apparently INFJ and some which seem very INTJ.
Factoring in his health makes it harder as he may have suffered from a brain malady, brain tumor or as has been "the official opinion" the clap.
I'm sure that would have an effect on the personality.
Is he using tertiary Fi or secondary Fe?
INTJ case would be supported by the fact that he's being very brutal against hypocrisy and that type of conviction is usually typical of Fi users, as you mentioned he does not state his values and he is clearly an nonconformist.
On the other hand there are other non conformists like Kiergegaard who is an INFJ. Could he just be value driven in general like an aux Fe would be?
One thing that perplexes me is his relationship with Wagner whom he idealizes but is later disappointed in and er...doorlams him

. That type of behavior I thought to be more typical for INFJs. (I can't believe I'm saying that...XD ) What is your take on that?
If he was mildmannered and agreeable in person wouldn't that itself indicate Fe?
The highly emotional tone in his work...is it a Fe user trying to influence and persuade the reader with nuances of feeling or rage from breach of personal values by "the herd"?
The obvious conclusion would be to rule out Fe as it is a harmonizing function, however I don't know..I suppose Hitler harmonized the Germans for his unpleasant ends but not all INFJs are out to harmonize and blend in (Kiergegaard for example, never liked...nor was Jesus if you really think about it unfortunately..) INFJs have a fidelity for their vision over the need to blend in, sometimes this causes a very real inner friction which can result in very emotional behavior.
Was he cold and unaware of emotions like INTJs are reported to be (correct me if it's %€"#%") or hyper aware of emotions?
Then I wonder: Is his reasoning Te or Ti?
Ti seeks root causes and pieces information into clusters.
Te soves problems in a systematic fashion.
It's hard to weed out the essence from the functions descriptions as they'd relate to this case. One description I found some while ago on this forum (I think) which I'm unable to locate (My apologies to the writer) was that when dealing with subjective matters, as Nietzsche's philosophy was (like reducing for example causality to a psychological affect "The Will to Power" ) , Te and Ti act in different ways:
Te orientated on subjective matters: Interprets a subjective conviction analytically from objective facts---> At the base there is an objective idea. Subjectively orientated thinking subordinate to objective data.
Ti orientated on subjective matters: Ti is orientated by it's nature by a subjective factor: feeling or direction. Starts from subject and return to subject---> produces new views, not new facts. Yeilds insight but not new facts. Facts collected for the purpose of serving as evidence or examples, not for their own sake.
The concept of the will to power is highly subjective, a psychological affect that colors our perception and makes objectivity impossible because of the constant contamination of subjectivity. Would that affect qualify as an objective idea by definition?
One biographical anecdote I'd like to offer is that Nietzsche did his thinking on long solitary walks. My superficial understanding would be that it would be more indicative of Ti but I'm not that naive, as it might just be indicative of Ni (???) Any thoughts on this? (<---I'm actually attempting to converse here. Kudos for me!)
Other factors that don't make it so clear cut for me that he was an INTJ are his prosaic style, lack of providing any objective evidence to support his theory. He was called "Prophetic, soothsaying, exaggerated and uninformed" (Schupforta) which doesn't scream scientific and precise to me. He mystical (argument for Ni) and poetic (I'd lean on INFJ...may any possible INTJ poets present not stone me...Amen)
As faults go INFJs are often said to be critical at their worst and INTJs selfish. It's hard to see which would be the case here as you could argue both sides.
His interests in philology, music (he composed and played piano), and religion sound very INFJ to me. His philosophy was said to have a humanistic bent and he valued psychology, claiming that it would offer the keys to philosophical problems. that said Sartre's philosophy was obviously centered around the individual as well. If I'd have the expertise I'd try to compare Kiergegaard-Nietzsche-Sartre to maybe analyze this further but I'm not. I enjoy reading philosophical works but have not analyzed them.
His secondary function would have began to manifest at twenty. Does it have a Fe or Te flavor????
His creativity peaked at thirty which is the time I've gathered we begin to develop our tertiary. I'd need more background info to see if it had a Fi or Ti tone. What would the experts say?
On the other hand the brusque style and reducing the affects specifically to the will to Power (strong willed Fi gripped INTJ reducing the world to WILL) could be blatantly indicative of INTJ as those are commonly attributed to INTJs. Then again is Nietzsche really self confident? Is his confidence the blossoming of a self assured individual bravely attesting to the firm Fi values or actually a Fe overwhelmed individual fighting against an impulse to fade into the perceived "herd" struggling to be firm and thus resulting in an exaggerated attempt to distance himself from the mass of non-self creating individuals?