@DJMcMayhem, Since you can't replicate, are you able to teamviewer into my maching? Meanwhile, I modified the first line to

syn match delimited /\\note{_.\{-}}%EndNote/

because my \notes cover multiple lines including expressions like \begin{itemize}, so I now have a uniquely identified closing delimiter. Exactly the same problem with the example, however. It's quite baffling that different machines are doing different things. I'm on Linux Xenial, but I can't imagine that would make a difference. If you are able to teamviewer in, let me know some times that would work.

@Tumbler41 YEEEEAHHH!

Thanks!

Do you actually need/want tex highlighting while you're doing this?

Try this:

syn match delimited /\\note{\_.\{-}}/ containedin=texDocZone

With that line, the @DJMcMayhem's example works for me

Actually, this is probably better:

syn match delimited /\\note{\_.\{-}}/ containedin=ALL

It was failing because the note was within an area that was already a syntax region/match, so the delimited group was not applied

adding the containedin argument allows your new group to be found inside other groups.

Works beautifully now, thanks very much to both of you.