My new theory is that Ni, especially NiFe, is all about self-consciousness. I mean, that's not the only thing it does, but one of the things it gives rise to is a life that notices the self.
Of course, the classical statement of self-noticing is Walt Whitman's Me Myself in section 4 ("apart from the pulling and hauling..."). But Harold Bloom is noticing the same phenomenon when he attributes Shakespeare's characters with the power of "self-overhearing," the ability to change based on what you hear yourself say (which presupposes the Second Self, the Self that watches and can order a change in the Primary Self, the Persona that acts. Or perhaps the change is in that Third Thing which does not have a name).
Maybe this isn't actually associated with Ni--and properly speaking, I'm not claiming that Ni IS self-consciousness, but rather than high-level, well-developed Ni can often manifest itself in this sort of, abstracted-from-myself self-looking or self-awareness. Similarly, low-level, one-dimensional Ni can manifest itself as a failure to be self-aware, to be aware of what is going on within yourself at a deep level.