Hello,
...you mean the taskbar tray?
The taskbar tray icon can be enabled and disabled by changing a value in the registry.
...This is not the same as the 'hide when inactive', 'always show', or always 'hide taskbar tray' icon settings in 'Taskbar and Start Menu Properties'. This will either enable or disable the entire functionality...
Go to Start > Run > Type regedit hit enter...
There are two keys, a user key (to specify whether the taskbar tray icons are enabled on the account you're logged into) and a system key (to specifcy whether the taskbar tray icons are enabled system wide, by default).
Depending on your preference, browse to either, or both of the following keys...
User Key:
HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Policies\Explorer
System Key:
HKEY_LOCAL_MACHINE\Software\Microsoft\Windows\CurrentVersion\Policies\Explorer
...and edit the following REG_DWORD value on the right...
Name: NoTrayItemsDisplay
...to one of the following numbers...
0 = Allow taskbar tray icons
1 = Remove taskbar tray icons