I think anything with a .desktop file in one of the standard locations for .desktop files would display, as long as the .desktop file itself didn't prohibit the display of that application. Here's an example. Note the line 'NotShowIn=KDE;GNOME;' keeps this application from showing in the Gnome applications list. Instead, it is found under Settings.
Code:
dmn@Sydney-VM:/usr/share/applications$ cat system-config-printer.desktop
[Desktop Entry]
Name=Printers
GenericName=Printers
X-GNOME-FullName=Printers
Comment=Configure printers
Exec=system-config-printer
Terminal=false
Type=Application
Icon=printer
StartupNotify=true
NotShowIn=KDE;GNOME;
X-Ubuntu-Gettext-Domain=system-config-printer
Categories=GNOME;GTK;Settings;HardwareSettings;X-GNOME-Settings-Panel;X-Unity-Settings-Panel;System;Printing;
X-GNOME-Settings-Panel=printing
X-Unity-Settings-Panel=printing
Keywords=Printer;Queue;Print;Paper;Ink;Toner;
X-Desktop-File-Install-Version=0.24
Sorry, I can't tell you why your Tweaks Icon wouldn't display in the array of application icons. It's not normal. But also check the 'Sundries' icon, although that seems unlikely it would be there.
BTW, the icons like 'Utilities' that group several applications are called AppFolders. You can create them with your own categories, but I haven't done that myself. I usually use the search box to run something.
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