Is an image set for the Background? If so, you'll need to delete the image, or use an alternative image which itself has a gradient. The presence of an image overrides the gradient setting.

The advantage of using an image is getting rid of the single-pixel border around the Taskpane that you get when using a gradient setting only.

No I'm afraid there isn't any image defined (the "Task Pane Image" property is greyed out.

That's a little misleading in SkinStudio - when an image is not defined the attribute name will be grey - you can still designate an image by clicking on the attribute name & designating an image in the dropdown list. Still, if no image is defined in the skin in question, the gradient settings should work. I'm puzzled, but would still try using an image with a gradient there; be aware it has to be rather large to display properly.

Hopeless...
I have checked everything I could think about...
No matter the options I'm setting in SkinStudio (image, single color, gradient), the task pane remains black and only black.
Is it possible that somewhere in my system, a setting overwites this skin setting ?

I'm not aware of any user overrides that would do that. This is very puzzling and I'm afraid my fund of knowledge here has been depleted. Hopefully, one of the SD programmers will see this & chime in. Might also be time for a formal support request to Stardock.