My Veeam backup & rep setup has worked fine for the last few nights, did the base full of my main PC, and two successful little incrementals. The backup target is a spanned volume on my spare computer, data flowing via a switch.
Now set up a task to wake the backup target machine at 00:50, the backup is scheduled to start at 01:00, then theres a wait for idle task which will send it back to sleep if theres less than 10% disk activity for 15 minutes (and it waits 15 minutes before checking for the condition as well)
So in theory, it will wake up at 00:50, the backup will start, when it finishes the wait for idle task will trigger, executing a batch file which sends the machine to sleep again, ready for the next night.
Or if the backup doesn't run for whatever reason, the target machine will wake up, idle for a bit, then go back to sleep.