Per the unision manual, the polite stop watching signal is SIGUSR2.
6.10 Interrupting a Synchronization
When not synchronizing continuously, the text
interface terminates when synchronization is finished normally or due
to a fatal error occurring. In the text interface, to interrupt
synchronization before it is finished, press “Ctrl-C” (or send signal
SIGINT or SIGTERM). This will interrupt update propagation as quickly
as possible but still complete proper cleanup. If the process does not
stop even after pressing “Ctrl-C” then keep doing it repeatedly. This
will bypass cleanup procedures and terminates the process forcibly
(similar to SIGKILL). Doing so may leave the archives or replicas in
an inconsistent state or locked. When synchronizing continuously (time
interval repeat or with filesystem monitoring), interrupting with
“Ctrl-C” or with signal SIGINT or SIGTERM works the same way as
described above and will additionally stop the continuous process. To
stop only the continuous process and let the last synchronization
complete normally, send signal SIGUSR2 instead.
It has a SIGTERM handler to exit gracefully. In general with file related tools, cleaning up would mean removing temporary files whose copy had not finished, plus unlocking any resources.
Implement and test a script that sends SIGUSR2, waits for a bit, and if still running sends SIGTERM. For example, if using a systemd on Linux service, the ExecStop script could send this signal, wait a bit, and check the status of syncing. Then the usual TERM signal from the service manager would ensure it shut down. Confirm your sets of files are intact. The sync program being crash consistent does not necessarily mean your files are all at the same point in time.
Seems like you have a backup method independent of the sync process, which is good.
I do not consider a sync like this alone to be a sufficient backup. Good backups are offline, immutable, and to different media. If accident or malware were to write bad data to one side, it would be synced to the other. And the sync conflict resolution could introduce complications, versus merely making an archive out of one tree.
An independent means of backup also provides assurances that your changes to the file sync procedure does not cause data loss. Worst case, grab backup archives, safely protected from writes.