So my paper is about a particular book and i'm referencing one of the appendices for my argument. The title of the appendix is Nagel's brain, and i'm trying to say the quote is from the appendix's/appendices' namesake, and i'm not sure which would be appropriate.
"Appendix" is the singular form. You are referring to one appendix's title.
Some style guides recommend consistently omitting the "s" after "x'" or "s'" when forming a possessive; some style guides recommend consistently including the "s" after "x'" but not after "s'"; and other style guides recommend consistently including the "s" after "x'" or "s'" in the same situation.
Technically the possessive would be either "appendix's" or "appendix'" ... but, like many other words, this construction is awkward and best avoided.
The appendix of Noah's Brain contains a chart which shows ...
If there is more than one appendix, you can refer to them by name / number:
In Noah's Brain, Appendix 1, there is a chart which shows ...