Sorry, but I don’t think you can get the toolbar control button using Swing. There are no appl-esqe features that would draw it for you. Try the apple.awt.brushMetalLook property, but as far as I remember, it had a single toolbar and title. SWT seems to be your only choice.
Also, I don't think you should worry about this user interface element. This button has been removed from all OS X user interface elements since 10.7 (Lion)
With Lion, most applications have a full-screen icon in the upper right corner. When using Swing to program on OS X, I think you should draw a line at some point in your quest so that it looks completely native.
To add to this, I think Mozilla clients are developed in Objective C / C ++ and some Java (maybe) for Mac.
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