I've been battling this question for a while now. It will sound very trivial I'm sure to an experienced Illustrator user but I've found it extremely hard finding any relevant info regarding it. All info I find about how to use the gradient tool is regarding either shapes or text and it can't be applied to my problem.
See in the image below to see the boiled down version of my problem. What I have is an ellipse shape and a path inside that ellipse. The path combined with the shape creates an area. Now, I want to add a gradient to that area, without having to close the endpoints of the path. How would I go about doing this?