Hi Edgepark,
I have attached two sketches here. The FFD as well the Cage Deformer can use Point selection, to store previous selected points. So the handling is not that complicated.
The other example uses a Shader Effector as Deformer and a Gradient to get this animation done. Have a look in to the file.
The second file contains my favorite, as it is perhaps simpler than the ones before.
The idea was to use the Falloff to limit the influence and to use the Gradient to adjust the effect. You can animate the gradient with the red or green Null, or move both with “their” parent. Of course the Gradient by itself can be animated or adjusted to your liking.
All the best
Sassi