Ahh … wellll … hmmm … that’s going to be a little tricky! Guess I shoulda anticipated that one. 🙂
One way you could do it would be to use Xpresso to use the sweep start/end parameters to drive the position of the gradient points, but that’s going to be pretty involved.
And easier way would be to use a texture in place of the layer shader in the alpha channel, and instead of actually animating the sweep, animate the texture tag’s Y offset position. The downside is that you’re not going to get a fade as the lines disappear completely. You can either hide that with spline/object placement, or you can add the effect in post with a little rotoscoping.
project file