Hey
JOGL is very low level. I advise you to create an image (JPG, PNG, ...) and to use it to make a texture in order to show the world map in your panel if this panel uses JOGL (otherwise, it's a pure AWT/Swing problem, just call Graphics.drawImage()).
Do your both panels use JOGL? Do you use a GLCanvas or a GLJPanel? There are several ways of displaying a background color in OpenGL, you can simply change the clear color (it works with a single background color but not for a gradient) or you can disable the depth test and draw a quad that occupies the whole screen (it works with a single background color, a gradient and even an image). This example should work (and isn't very difficult to port to Java/JOGL):
https://www.opengl.org/discussion_boards/showthread.php/164345-Gradient-background?p=1161267&viewfull=1#post1161267Have you ever used
Worldwind? Its Java implementation uses JOGL under the hood, maybe it would help you not to reinvent the wheel.