it's interesting that the three of them kind of represent a
"dark triad" of negative personality characteristics: Coyote the charming manipulative sociopath, Loup the vulnerable narcissist, and Zimmy the paranoid borderline. Of course, all three of them are capable of acting benevolently as well, because GC doesn't have villains.
My read is Coyote as dark triad (powerful, manipulative, best to steer clear altogether but has ways of achieving the otherwise unachievable, things can be good when he's happy) "Loup" as long-term narcissistic abuse survivor/bully cycle (as long as he's entranced by dark triad tactics he's stuck there) and Zeta as something like a broken hyper-empath (control issues, anger, antisocial, sleep disorder, self-erasure).
That's reasonable. I was thinking specifically of the "vulnerable dark triad," which is focused on the propensity for self-harm, rather than the traditional dark triad which is focused on harm towards others. But of course no real-world behavioral schema is going to perfectly describe a bunch of gods and superbeings. (Nor will it perfectly describe real people, for that matter.)
Anyway, let me try to describe them more in terms of traits than labels.
I see Coyote as sociopath-ish because he has a weak sense of self and limited affective empathy. His emotions, especially the negative ones, are superficial and short-lived. He enjoys being as not-himself as possible, by borrowing other creatures' lives and seeking suicide. The thing that brings him back from the roles he plays is not a love for himself, but simple boredom; ultimately, other creatures' lives are as unfulfilling as his own. However, he does enjoy seeing other beings discover
their true selves, perhaps because he hopes to vicariously experience their self-love. This motivates a lot of his pranks as well as his (fairly responsible) management of Gillitie Wood, dividing the Forest from the Court and helping individuals move between the two worlds, so that everyone can become what they want to be without interference from the other side.
I see Loup as vulnerable narcissist-ish because he has an unstable sense of self. He
wants to see himself as a perfect being, but this image is threatened every time someone challenges his power, wisdom or authority, and he responds with rage and terror. He loved Lana because she reinforced his ego by loving EVERYTHING about him, and that gave him the security to risk being nice for a change. With Lana's (apparent) death, he no longer knows who he is and it's back to angry freakout mode.
I see Zimmy as borderline-ish because she has such a negative sense of self, and because her interpersonal relationships run so hot/cold. Gamma is the best person ever and her savior and and she'll do anything to keep Gamma from abandoning her; people who are less close to her and understanding of her, like Kat, are positive threats and their very gaze is painful and self-erosive to her. And
she, of course, is worthless garbage that everyone else rightfully wants to destroy. Her affective empathy is high, but distorted and selective; she feels the negative emotions of others much more strongly than the positive ones, and usually
personalizes them to be about her. (
Studies suggest that people with BPD are often "broken hyper-empaths" in this way.)
Each of our three protagonists shares psychological traits with one of the above people, but has learned over time to incorporate them into a healthier and more pro-social life.
Like Coyote, Kat has a weak sense of self; hence her carelessness for her own safety, her comfort with body-modding, and her ease of interaction with humans and nonhumans alike.
Unlike Coyote, Kat has very high affective empathy, so she works much harder to make other people happy and free from unnecessary suffering. Kat also appreciates other selves more fully than Coyote does, which drives her need to help others self-actualize and safeguard their autonomy.
Like Loup, Annie has an unstable sense of self; hence her tendency to fracture into multiples, and her extreme anger, anxiety and confusion when her understanding of herself is threatened. (Mother's killer or loving daughter? Father's shame or dutiful daughter? Mort's girlfriend or independent loner?)
Unlike Loup, Annie has enough empathy and dignity to be concerned about these tendencies threatening the consistency of her behavior and the well-being of others. So she's put a ton of work into improving her self-discipline, and she utilizes her own experience of altered/fractured states to become a better Guide and medium.
Like Zimmy, Renard has a highly negative sense of self; hence his shame, self-loathing, desperate attachment to a partner that can serve as a "better half," and fear of freedom and returning to his old nature.
Unlike Zimmy, Renard strongly feels the positive emotions of others, so he has much more capacity for trust and friendship. (Zimmy loves and needs Gamma, but she has very little faith in Gamma's love for
her.) Renard also compensates with a strong code of honor: he may not be proud of what he
is, but he can be proud of what he does.
Well, Tom has mentioned that
if Zimmy's parents could remember her, they'd be glad that she's gone. Whatever their reasons for that, it certainly sounds like severe abuse/neglect from
her point of view. Of course, past trauma can lead to retraumatization in later life, and Zimmy's powers strengthen that feedback cycle.
I'd also say that Zimmy's being conscious of her own toxicity is more delusion than genuine awareness. She's unshakably convinced of her own global horribleness, which makes it very hard for her to recognize which aspects of her behavior really
are a problem. Gamma tries to help her with that, but when
Annie last met them Gamma looked like she was doing
very poorly, and Zimmy was apparently too wrapped up in her own fears to notice.
Annie's eloquence on this page probaly strikes some people as unrealistic - like a rehearsed speech, as opposed to how people really speak, especially 17-year-olds. But it is NOT out of character for the GKC Annie.
Yeah, she's a professional medium and semi-professional guide. Annie knows how to talk to people, as long as it's not about
her feelings.
A browser cache issue, maybe. 
Thanks for pointing it out! 