Proposed definition #3: Orientation by manner of orientation
Introverted Intuition is a way of orienting yourself to your environment by consciously attending to the expected interpretations of things. In this manner of orientation, you hold agnostic about whether those interpretations are true. You view them as expected interpretations, nothing more. Your world is a world of expected interpretations defined by others; you navigate through those interpretations and use them without regard to whether they're true, always keeping the interpretations separate in your mind from the actual objects.
For example, whereas from an Extraverted Sensation perspective, you might feel very impressed upon meeting a man wearing a fancy Italian suit (signs call forth a natural response and need no interpretation); from an Ni perspective, you would consciously say to yourself that he's wearing an Italian suit and this is supposed to make you think he's wealthy or upper-class or really has his act together or something like that, and therefore is supposed to make you feel impressed (signs and what they mean are connected only arbitrarily). Whether he really does have his act together is a matter upon which you reserve judgement. Consequently you don't feel impressed. You merely note the expected interpretation as no less a part of your environment than the suit itself.
As a language of Ego Orientation
As a Dominant Function, Ni leads INJs to anchor themselves primarily in discovery of and attunement to that "what else"--to seek communion with it for its own sake. INJs are typically concerned with finding an independent and all-encompassing perspective on whatever interests them, so they can see it without bias, without being fooled or led along by ways in which other interests have set things up, and without a merely partial understanding.
As a Secondary Function, Ni typically leads ENJs to be aware of alternative ways of negotiating the social world, that exploit the assumptions that people make in order for there to be a social world. One might use this awareness to be on guard against cheaters, to prevail by setting knots and traps for others to fall into, to commit to a vision that might currently seem impossible, or a thousand other ways to serve or create an Extraverted goal.
As a Tertiary Function, Ni typically leads ISPs to suspect others of hypocrisy and cheating and putting on appearances aimed at exploiting people's credulity--especially hypocrisy inherent in social institutions. Sometimes ISPs draw upon Ni to find ways to throw a monkey wrench into social systems that call them into some kind of obligation: to respond in ways that don't make sense within the system's explicitly stated ways of interpreting behavior as cooperative or hostile (but are indeed hostile).
As an Inferior Function, Ni typically leads ESPs to either self-doubt or claim to a mystic vision--to see themselves as an oracle of transcendent truth, bypassing the need for finding things out through observation, reasoning, and putting ideas to a test.
Naturally, you can see plenty of dominant-style Ni in ENJs, secondary-style Ni in INJs, and so on--even inferior-style Ni in INJs.