[This answer was written sooner as a reaction to the discussion broke in comments to @Chelonian's answer, than as a focused answer to the OP question. So it may look off-topic. Yet I've decided after some hesitation not to remove my response. As a particular, phenomenologic p.o.v. (seeing mind-body dilemma as a false one), it could be of some interest, and to me it is certainly not off-topic]
When I'm jerking back my arm from this boiling water in front of me, I automatically take my that action upon myself. Not I started the movement (but subcortex and muscles) but everything looks like (and not the other way) just 1/10 sec later as if it was me who thought out / decided to withdraw. Such is the property of pre-reflective consciousness (but not of my Ego, mind) - to "ascribe" everything to oneself; and that consciousness is anonymous, faceless.
But where is freedom here? So far we see only responsibility, or taking any "guilt" upon oneself. The freedom is in that the meaning of the situation, - including of my action, for the start of which I wasn't responsible objectively, - wasn't determined by anything (while the jerk was determined at its start), it was a random selection by spontaneous consciousness of one possibility out of some possibilities. Might I have not withdraw my arm? I wasn't in the power to at the beginning of the movement, right; but I might have quickly catch it, deciding to endure, or, 2 sec later might have return the arm back in the boiling stream. Also, I might have scream as I were jerking it or might have simply open wide my eyes. A continuation, development ot the primary bodily reaction was tied with and correlative to the meaning; but the latter was applied by my consciousness freely by selecting from a number of possibilities (of being me-in-the-here-world) implied in and admissible by the circumstance.
What does it mean that was "free"? It means it was in the regime of dissociation from the givenneses provided to consciousness, i.e. in the mode of their annihilation. The hot stream, and the pain, were highly appreciated - exactly in order them not to meddle in the sudden decision. Consciousness feels that it doesn't base itself on anything when it chooses.
May there be that this "freedom of choice in void" is just an epiphenomenon, consciousness' illusion, and really that some data, stalking unobserved, have determined my choice over the meaning and the action? Yes, that may be, but I'll never know that myself. Other people might tell me this later, or I myself might say it in explanation to myself, - but it never will be evidence (like the sense of freedom was) and never become credible enough: it will be a matter of trust (like all theories of objective reality are).
In what way can the above text seemingly unrelated to the OP's question be relevant nevertheless?
"I know those experiments pretty well but I would argue that
initiating moving your hand can indeed be done by any robot but
initiating writing a sentence about your consciousness which turns out
to be true is more plausibly attributed to the consciousness itself
than to deeper levels which aren't conscious."
But I've argued (from a perspective close to be Sartrian, as I hope) that even in experiments of automatic reactions such as ticks or reflexes or robot-induced moves - we remain fully free. Therefore contrasting simple automatisms with "writing a sentence" about subjective experience, i.e. the complexity, is not a way to prove qualia of consciousness or disprove determinism. The "more plausibly attributed" argument is not, to me, a right way to defend against @Chelonian's arguments.
Just consciousness with its freedom and mechanics with its determinism are two nonintersecting domains, neither of the two can penetrate the other to strike. They also are on different levels: I agree with those saying consciousness is an ontologic concept (i.e. it exists before [individual] world is possible), while mechanics (in wide sense of the word) is ontic: it needs entities already existing, and it implies there is "reality" totally independent of consciousness (so it is another reality than that consciousness could inhabit).
In my comments to @Chelonian's answer (all comments therein are found now in chat) I've expressed the opinion that a brain (neurons) or a computer can never (or at least in our age having our baggage of outlooks and ways to formulate thought) be conscious, even if it is much more clever than man at tasks and learning; because computer cannot conceive of, say, 2<>2 (break of self-identity of an entity) whereas man's consiousness does it every minute.
"I am a conscious being with a true first person perspective"
According to Sartre (see "The Transcendence of Ego") cartesian cogito ergo sum is a performative fallacy: who thinks this thought (active, pre-reflective consiousness, me) is not whom the thought is ascribed to (I, an inert reflective object). From this particular point of view, having "first-person perspective" designates not the consciousness but one of objects of the world, and it could be removed from the phrase as redundant. Then you are left with "I am a conscious being" which sounds similar to "cogito ergo sum". And that will suffice.
When you are writing down that phrase you actually don't have the first person perspective because your consciousness is busy with writing a sentence. But you remain conscious (and free). You're keeping a dim purpose what you are writing for, and your movements and auxiliary thoughts serve that goal. Consciousness understands itself and what it is doing, even though there isn't any Ego currenlty here or Ego is seen in the past as if remembered other man. Because positional consciousness of an object or one's activity is at the same time non-positional consciousness of the self. That primordial self-consciousness (which is difficult to catch) - without being an object to oneself - is a primary evidence and needs not be proven, especially by subconscious "spooks" or neurons as "spooks".