I'm Plugged Into a Robot Who's About to Kill My New BF and It's Taking A Long Time AMA

Washing dishes, keeping the penguin fed, household stuff like that.

Never swam in piss but it smells like orange tang

Well, there's this open access edited volume Anime Studies: Media-Specific Approaches to Neon Genesis Evangelion; it's not generally about that, but there might be some tidbits (and relevant to the OP, there's a chapter entitled Creating Happy Endings: Yaoi Fanworks as Audience Response to Kaworu and Shinji’s Relationship).

More relevant to your question, here's a random assortment of Google Scholar results:

My Father, He Killed Me; My Mother, She Ate Me: Self, Desire, Engendering, and the Mother in Neon Genesis Evangelion
Boy with machine: A Deleuzo-Guattarian critique of Neon Genesis Evangelion (full text available on Sci-Hub, just paste in the DOI: 10.1353/mec.0.0010)
Japanese Science Fiction in Converging Media: Alienation and Neon Genesis Evangelion (couldn't link directly to the PDF and the Academia.edu page would require a login, so I've linked the Google Scholar result which will take you to the PDF if you click on it)
Exegesis and Authorial Agency through Judeo-Christian Iconography in Japanese Anime: Neon Genesis Evangelion (1995-97) as an Open Work
You Are Not Alone: Self-Identity and Modernity in Neon Genesis Evangelion and Kokoro

Like the themes of the robot I'm stuck in? You're weird

How many neo tokyos have you saved?

Yeah it's true

However this scene in particular has a pretty dramatic impact imo