I searched for a long time for a convenient way to minimize Thundirbird into the tray under Gnome. Thunderbird itself does not offer this option.
The first try was to use the extension moztraybiff. moztraybiff utilizes the standard systray as specified by freedesktop.org thus supporting Gnome, KDE and IceWM. moztriffbay shows additionally to the “normal” Thunderbird window a systray icon that is also able to indicate new mails. The problem I had was that the Thunderbird was still in the taskbar and the window list when switching windows via Alt-Tab.
So I looked for another approach and found kdocker. kdocker is able to minimize any application to the systray of Gnome, KDE, XFce, fluxbox, ... . Unfortunately it depends on qt, so you might not like it when pou have to pull in qt just to use kdocker. To use kdocker with Gentoo Linux and then Gnome (my personal favorites), this is the way:
Download the ebuild for kdocker and place it in your portage overlay. For a detailled manual how to do this see this article in the Gentoo Wiki. There is only one pitfall you have to take care of: The ebuild was saved with windows newlines that at least cause errors with recent testing portage versions. So just run this command first before starting with the above howto:
cat kdocker-1.3.ebuild | tr -d “\r” >| kdocker-1.3.ebuild
Then the ebuild will be ready. After you installed kdocker, you can add the command kdocker -e -b -l thundirbird to your Startup Programs in Preferences - Sessions. This will automatically launch thunderbird at gnome startup. From now on, thundirbird lives in your systray as desired.
The disadvantage of this solution is, that there is no notification of new mails and that you cannot use the close button of the Thunderbird window to minimize it to the systray (as you might be used to in other applications) since this closes Thunderbird and kdocker. Just use the minimize button instead.