Something that works some times and doesn't work other times.

Two Windows 10 computers on the same workgroup and signed into the same Microsoft account and operating through the same router and sharing the same Internet account. All Windows 10 sync settings are turned on for both computers and network discovery is turned on for both computers.

Sometimes when the wallpaper background is changed on one computer, that background also changes on both computers. However, at other times when the identical action is taken, the change of wallpaper on one computer will have no effect on the other. There's no apparent explanation of why this does happen or does not happen.

This is not a problem. Rather, it's an unexplained mystery that appears to be unsolvable.

When I posted the question in a Microsoft forum. one of the "MSFT" experts insinuated that wallpaper syncing does not work regardless of what others say. The response was "Wallpaper synchronization is done on a lazy basis so that we don't get in the way of other system activities. I would not expect it to be able to be used to synchronize two systems. You could turn off synching and instead manually set each to be equal to the other, though. :)"