You're on the right track... from the ArchWiki:
For starters, you can flag packages out-of-date. If it stays
out-of-date for an extended period of time, the best thing to do is
email the maintainer. If there is no response from the maintainer
after two weeks, you could send mail to the aur-general mailing list
to have a TU orphan the PKGBUILD if you're willing to maintain it
Another option in the meantime, although this might not be a preferred practice... but, I have seen some users edit the PKGBUILD and then upload their version to a pastebin and then link to it in the comments. Other users will still need to make manual edits but at least the update will be known.