6th function is the opposing attitude to your auxiliary function, i.e Ti in an INTJ.
Here's a solid writeup on the 8 function model:
Understanding the Archetypes involving the eight functions of type (Beebe model)
This is a writeup on the 6th function specifically, in numerous types - pretty broad, but it's good:
Power of the 6th Function – Leon Tsao
If anyone wants to get further into John Beebes 8 function model, I would highly recommend a book called Depth Typology
by Mark Hunziker - it does not describe the functions in detail, we can understand the functions easily enough by ourselves or with the aid of about a million other books - but it goes into detail regarding what the 8 function model is, why it's a better alternative to the 4 function model, and it explains how each of the 'shadow functions' manifests - what their role is, how they work, when they might appear etc etc, it's a brilliant book.
My own, admittedly limited, understanding of the 6th function is that it basically makes you irritable and grumpy if you're forced into it - a simple example would be the one in the book - an INTJ who has to microscopically examine virtually every phrase to comprehend it's meaning, as well as the basis for the statement, all it's implications, and the possible unintended consequences of saying it one way versus another.
On the surface, people with a limited and flawed understanding of typology might think that looks like Ni, dude isn't an INTJ, wah wah wah, but no, it's Ti that he's having to use - Ni doesn't want to microscopically examine shit, it wants to sum things up and get the gist, it doesn't want to explore in detail and then dissect all possibly meanings of a statement and search for all possible implications and unintended consequences - it just gets the 'gist' and comes to one singular meaning.
In that example, essentially, the INTJ is forced into "defining" words and phrases to an extreme degree - defining
is the realm of Ti. That kind of in-depth scrutiny is something an INTJ will not
want to do for extended periods of time, or it'll piss them off and make them grumpy.
An INTJ would want to read something, just think boom, here's what it means, here's the long-term ramifications, and be done with it (Ni-Te).. they don't want to be forced into that kind of defining
work, where they're going over every word, every phrase, dissecting any and all meanings and possible implications etc etc.
Imagine say.. and INFJ having to use their Fi instead of their Fe? Oh right, easy to imagine due to the infinite mistypes.
Okay try again. Imagine an ISFJ forced into making a decision via Fi rather than Fe - having to rely entirely on their own interpretations of what is good/bad etc, they would feel lost and get irritable, it's not natural for them, it's not what they want to do.
To go full hardcore stereotype, picture an ISFJ mum who has to buy something for a kid - no problem, right?
Now picture they have absolutely no idea what that kid likes. That kind of thing right there would irritate an ISFJ (and an INFJ
They would be forced into buying something they personally like and see value in, rather than what someone else would value - this is hard for them, they don't want to do it.. "how do I know what little Johnny likes?" "will he like this?" "is he into Paw Patrol?".. it's a terrible stereotype and example but I'm hopeful it conveys the message relatively accurately.
With the 6th function, comes fear and shame. The INTJ in the above example would feel shame for not being able to to that kind of defining
work (Ti), the way it needs to be done (Te).
The ISFJ would feel shame for having to buy something she personally likes for someone else (Fi), rather than something she knows they would appreciate (Fe).
IMO, the fear comes in as a fear of how will this be received - how will the work they've done using their 6th function be received in the outside world, how will the INTJs defining
work be received? How will the ISFJs Fi present be received?
The 6th function is highly critical of yourself and others as well, it's not a function you want to use at all, if possible, it's not a function that should be developed or worked on. It should be replaced with your auxiliary function at all times, if you can recognise yourself resorting to your 6th function.
So an INTJ might use Ti
when criticising someone - dissect their arguments to the enth degree and make them feel stupid.. this isn't their Te being blunt, Te in an INTJ is positive (usually), it's their Ti being a prick, for example, and it will also criticise the INTJ themselves which is why they feel the fear and shame associated with the 6th function - this kind of behaviour will appear when ones competency is questioned - that's
when the INTJ would shift into Ti mode to tear your argument re: their competency to smithereens.