Windows 10 - System Tray Icons Won't Hide
Solution 1:
I discovered the solution by trial and error / accident.
Google-fu suggested that this registry key:
HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Policies\Explorer
was related to numerous Tray related problems so I looked there and found a REG_DWORD entry labelled:
NoAutoTrayNotify
which was set to 1. I changed it to 0 and restarted Explorer et voila my system tray starts working again. I've no idea how this got set in the first place, but I'm happy now anyway.
This link tells us "This setting determines whether the items are always expanded or always collapsed." which sort of suggests it should be controlled by the Win10 option "Always show all icons in the notification area", but toggling that option had no effect for me - even with Explorer restarts.
Solution 2:
A new "sneaky" feature of 1809 (1803?) allows one to hide icons into the area above the up-arrow thus:
Drag them from the taskbar and hold them over the up arrow, whereupon the window opens for the icon to be popped in a location of one's choice.