Of course, this only proves a reaction to the futile challenge of proving you have free will (the cause of the effect).
We wouldn't be questioning whether we had it or not if we didn't. We couldn't. One of the finer points of the self-evident is that, not only does it not require proof, it cannot be proven. It is pre-logic. Logic is a method of guaranteeing that one's mental contents conform to the facts of reality, and are consistent with other mental content. If there were no room for error, nor room for correcting error, it would be because our the functions of our consciousness automatically conform to reality (as it does in animals, who, if you've noticed, do not question their mental processes or content).
The introspective data available to support the self-evidency of consciousness is the effort required on the part of the observer at the base level of consciousness: we do not automatically know what we're observing; we have to volitionally exert the required energy to understand. Staring at a physics text will not teach you phyics. Reading it with a fully engaged attention, consciously differentiating and integrating the information within the context of data and experimentation, and comprehending how it makes sense as opposed to other explanations of nature is not something that happens unless you make it happen.
The argument you're using to evade this (that
science says you can't control your own thinking; how you can have science without self-initiated, self-monitored mental focus is a complete mystery, apparently
) relies on an acausal representation of free will. It demands that decisions be made without the employment of any prior knowledge which the conscious mind has programmed into the subconscious; that every time someone make a choice, they either relearn the entire intellectual context required to make a particular decision (and immediately, in the present moment), or that they do it completely blind (spontaneously), neither of which would do a damned bit of good in fulfilling the actual purpose of being conscious in the first place (that purpose being to maintain the survival of the organism possessing said consciousness).
Free will is not the ability to make decisions in a vacuum. It's the ability to control one's attention for the purpose of developing a conceptual grasp of the world. This is almost a mirror image of the religious claim that to be truly free, a decision has to be unrestrained by the material world. Is this the nonsense that Sam Harris is peddling? Lol.