In the Shape Fill > Gradient parameters, you could link the gradient End to the Start and use a Link > Scale of -1. This way, you only need to change the Start XY.
For a method that lets you easily rotate the gradient through any angle, give this a try:
Add a Gradient generator to a Group. Add you Shape to the same group and duplicate it ("Shape copy") if you need an outline — otherwise, you can skip this.
Link the Gradient Position to the Shape Position.
Set the Shape Fill to Color. Turn off the Outline.
Set the Shape Blend Mode to Stencil Alpha. [Make sure the order of objects, bottom up is Gradient below Shape below Shape copy].
Set the Group > Blend Mode to Normal (you do not want the Alpha to "pass through")
Set the Shape copy to Outline (only)
Link the Shape copy parameters you need to match the Shape, like Shape > Size, Shape > Roundness, Position, Rotation, Scale if needed, etc.
However you animate or change the shape (or if you decide to simply animate the parent Group), the Gradient and the Shape copy will "follow". If you're publishing a template for Final Cut, you can publish the Gradient generator Rotation > Z to change the angle.