What's the issue again?
cursor.position = get_local_mouse_position()
print(cursor.position)
Using a print statement like that right after assigning that local mouse position there, I get values printed to the console that are clearly the correct mouse position.
edit: ok, I think I know what your issue is. 🙂
The sprite you use for the mouse cursor has it's pivot/origin at the center of the image. You want to have it moved over to the point of the arrow.
Notice on the toolbar the icon in blue? That's the tool for moving the nodes origin/pivot point. In the above screenshot I've already moved it(the red-white cross) to the 'point' of the arrow, but when you open your project and highlight the cursor sprite node you'll see it's still in the middle of it.
