Nice take, I bolton. I agree with much of your analysis. As I always say when it comes to using character archetypes as analytical tools, there is no right or wrong answer. We glean from stories what we sense them to be. My take:
Nemesis: I agree with you re Hoyt (who fires Arthur) and I’m tempted to put Murray Franklin in this category because there is the Act Three showdown between Arthur and Franklin. And certainly, the way Franklin mistreats and ridicules Arthur creates problems for Arthur. However, ultimately I think Franklin is a False Mentor. Originally, Arthur perceives him to be a father figure, often aligned with the Mentor function, but he turns his ‘wisdom’ against Arthur. He speaks the truth to Arthur when Arthur appears on Franklin’s show, conventional truth I guess you could say, but Arthur at this point has turned against Franklin and that truth does not align with Arthur’s emerging shadow self.
To me, that’s his Nemesis: Arthur’s shadow, the rage and instinct for violence, the madness within. He fights it, he resists it, he tries through medications and behavioral modification to keep it bay, but ultimately, he loses the battle. Much like Travis Bickle in Taxi Driver and Jack in The Shining, who also lose the battle with their shadow, Arthur embraces his the Nemesis aspect of his psyche, represented by the shadow dynamic, and in effect becomes a Nemesis.
Mentor: The Social Worker strikes me as a True Mentor were Arthur to persist in following the path toward a conventional life, but eventually she is helpless due in part for bureaucratic reasons and more significantly, Arthur giving himself over to his growing madness.
Trickster: I like your take on Penny as a Trickster, that’s a pretty easy call in my book.
Of the major characters, that leaves Thomas Wayne and he strikes me as another father figure. Indeed, in the end, we don’t really know if he actually is Arthur’s father. His explanation about Penny’s unstable mental condition seems plausible, but you never know! In any event, I think he provides a similar narrative function as Murray Franklin, so another False Mentor.
Thanks for taking the time to provide your analysis. Good insights!