@DBMandrake I spent some time today reading the documentation on systemd. I think that to be consistent with the corresponding service, the filename needs to be rc-local.service.d instead of rc.local.service.d (i.e. dash instead of dot).
Once I made the change, I was able to remove the artificial sleep statement in rc.local and my process still worked fine - presumably waiting for network before proceeding.
I can also see that rc-local.service correctly recognizes the new dependencies:
osmc@osmc:/etc/systemd/system$ systemctl show rc-local.service | grep network Wants=network-online.target system.slice After=network.target network-online.target systemd-journald.socket basic.target
Thanks again! Next I’ll look into defining a whole new service just for my script, removing it from rc.local altogether.