Yes, if I may repeat my point so I can work from it. I wrote:
under the principles of science consciousness is neither necessary nor not (contingently) necessary for movement, but necessarily cannot affect matter at all.

I was trying to be precise but generated a confusion. But my point is still well made.

There are two descriptions of necessity at work. 1) The contingent necessity that makes the rabbit be behind this tree if it is not behind that tree, and 2) the logical necessity that makes it impossible for the colour or image of the rabbit to be behind any tree. 1) has objects of the same ontological type, and 2) has objects of different ontologies. Necessity must be couched in terms of ontologies.

Consciousness is, I hope everyone will agree, not a player in a (purely physical) description of movement. This isn't because consciousness is not necessary for movement in certain (contingent) cases. Nor is it because consciousness is necessary for movement in certain (contingent) cases. Rather, it is because consciousness necessarily cannot be a player in any physical description whatsoever. 
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The principle by which science claims that consciousness cannot affect matter at all is more a mission statement based on the unrestricted privilege granted to empirical, physical, objects. The idea that "mind affects matter" simply is not countenanced by science, and if in some nook or cranny we find it so countenanced, we also find no empirical evidence.
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There are two causalities at work "in the head". This is because there are two ontologies (object behaviours) at work. One is physical, empirical, measurable, reciprocal - where A affects B and B affects A. The other is non-physical, not measurable, non-reciprocal  - where A affects B but B does not affect A. It is for this reason that we say that consciousness does not cause movement. We do not have the power to spark the neurons of our brain by thought alone.

With reference to the term "response": objects of consciousness (like colours, sounds, intentions) identify movement to be a response. They do not cause it to be a response. On the other hand, a physical description can only identify movement. Responses are not physically measurable, not because of any physical contingency, but because there are no physical parameters that can distinguish between a response and a movement.