Actually Jim your comment shows just how confusing WOL setup can be!
First, WOL has been working fine from my Client to the Server except when the client is left running, and the server goes to sleep. Then the Client can't wake the Server again.
It is actually impossible to set the "Allow this device to wake the computer" flag unless the "Allow computer to turn off this device to save power" is ticked. Both the second and third items in that dialogue are greyed out and unavailable if the first flag is not ticked, as per my image.
Ticking the "Allow computer to turn off this device to save power" flag allows the computer to turn off the network adapter when it is not in use.
Ticking the "Allow this device to wake the computer" flag, which has become active when the first flag was ticked, tells the computer to set the network adapter into a low power mode, which allows it to accept Magic Packets and fully wake itself, and wake the PC.
I was testing if WOL would work better if I never allowed the PC to turn off the network adapter, even when it went to sleep. But as I suspected, unticking the "Allow computer to turn off this device to save power" effectively means that the adapter goes to sleep when the PC goes to sleep. The adapter is never put into the low power state required for WOL. At least, with that setting unticked my client PC could not wake the server even when I restarted the MC Client while the server was asleep.
So, my test failed, and I was not able to get an already running MC Client to start a sleeping MC Server.
Basically it appears that when a device running MC is woken from sleep, thus activating MC again, MC does not successfully send Magic Packets to wake a Server, if it is asleep.
Also, if a Client is open and connected to a Server when the Server goes to sleep as there is no activity, then the already open Client also does not successfully send Magic Packets to wake a Server.
I am assuming here that MC actually makes an attempt to send Magic Packets in either situation above.
I would have to start using a packet sniffer to confirm if the MC Client in both the above situations actually sends Magic Packets. For the moment, that is above my pay grade.