Having written the book (with its eight function model framed in terms of a ship crew or lasagna) before Beebe's more common model had become more known, she later began addressing the theory, which you can see archived here:
Also, I at one point, approached her on Personality Pathways, and you can see the three part response here:
Carl Jung Psychological Orientation | Lenore Thomson Bentz
Another Q&A she did with some else on that site:
Jung MBTI Theory | Lenore Thomson Bentz
Our discussion went way beyond that page, and she clarified, among other things, some reservations regarding Beebe's model (especially regarding some of the "shadow" archetypes), and emphasized that this model is really all about "complexes". A complex is what is "constellated" when the archetype (a collectively held set of emotionally freighted imagery), becomes personalized, by filling up with each person's own experiences.
This made the whole thing easier to understand, for most everyone has heard of complexes, and the way some others have put Beebe's model out there; it's the functions themselves that "do" everything, and the "archetypes" are just these roles the functions fall into.
But having read up more on various Jungian concepts, a "complex" (or "ego state") can basically be thought of as a lesser sense of "I" working under the ego, which of course is our primary sense of "I". One or another will usually be in executive control, and the ego is the one usually in control, but others can come up and take over. Hence, as Jung says, "you've heard that we have complexes, but many don't know that complexes can have us".
It's basically a lesser form of "dissociation", which becomes "multiple personalities" disorders when it is not regulated well enough.
Again, this makes the whole thing easier to understand. The functions are just the perspectives held by these "I"s. The dominant or Hero will operate through the dominant function and attitude. In my case, approaching life through judging things true or false (T) by what I have learned individually or from nature (i). The Parent will be about "support", and connect with the auxiliary function.
So when we say something about "My Trickster did this, with this function...", what we are saying is that a part of ourselves; another "I" in effect, that is not usually in executive control [it's largely unconscious; hence, "shadow"] has surfaced because we feel double bound, and it tends to see things in the function opposite from the auxiliary, but with the same attitude, which is then used to in some way turn the table on the threat (to place the other person in a double bind, or at least to get yourself out of it. That's the "trigger" and purpose of that particular complex).
So this is basically what I learned through her.
So I would love to see her write another book covering all of this. It would really bring a lot of understanding to the theory.