zsh: confounded by zshcompletions

This command in my .zshrc works, providing the desired file completions for the note function:

compdef '_path_files -W "${NOTE_HOME:-${HOME}/notes/}" -g "^.*"' note

From what I can understand—which is very little—from docs and other sources, is to have completion definitions loaded automagically, there should be a file named _note in a directory included in $fpath.

OK. But, aside from the file starting with #compdef, I have no idea what I’m supposed to put in it.

This doesn’t work:

#compdef '_path_files -W "${NOTE_HOME:-${HOME}/notes/}" -g "^.*"' note

I tried removing the single quotes:

#compdef _path_files -W "${NOTE_HOME:-${HOME}/notes/}" -g "^.*" note

I tried running the _path_files function after the first line declaration:

#compdef note
_path_files -W "${NOTE_HOME:-${HOME}/notes/}" -g "^.*"

I even tried just copying the same command to the _note file:

#compdef note
compdef '_path_files -W "${NOTE_HOME:-${HOME}/notes/}" -g "^.*"' note

Nor does this variation work:

#compdef note
compdef '_path_files -W "${NOTE_HOME:-${HOME}/notes/}" -g "^.*"'

None of the completions defined in functions starting with _ in /usr/local/zsh/5.9/functions seem to offer a simple example I could mimic. Even searching the internet for _compdef _path_files doesn’t yield much aside from copies of things I’ve already read without finding an answer to my question.

This should be easy, right?