I've yet to meet anyone able to do so coherently.
You've also presented no argument for why it is impossible to define. If free will is possible, there should be no reason you can't define what it is.
If we have no free will we are just like candle flames; any argument that says we are more than candle flames is not valid when you assume we are candle flames.
People forget that logic requires axioms.
If I were to ask you to act a certain way and you do, this would neither prove nor disprove free will, because it tells me nothing about whether causality required you to act that way or differently and whether or not you deviated from causality, and so your analogy is meaningless. It is not what we'd ask you to do in order to prove free will.
You're using an assumption about an invalid argument as an argument in favour of free will, and that's no more valid than the original invalid argument.
To prove free will you need to prove that there are decisions in the brain that does not follow a) strict causality, b) randomness, c) any combination of the two. As you've pointed out, experiments where you ask a subject to act in specific ways do not produce evidence for it, as they can just as well just be causality in action. That the strawman hypothesis you presented is not valid does not prove the inverse, nor does it release any obligation of proponents of the idea of free will from providing evidence, or even just a definition to support their idea.
Free will is an absolutely extraordinary claim in that respect, because it implies a third category of events that is not a mix of strict cause-effect chains and random events, but introduces a "will-effect" chain that has no direct causal link but at the same time is not random.
As it stands, without a definition, the notion of free will is not even a fanciful hypothesis - to suggest it is a hypothesis would imply a fully formed idea. But the concept is so woolly and meaningless it tells us nothing.
It's at most a fervent wish or hope of not being an automaton. But a wish is not evidence, nor an argument, or even a hypothesis.
If you want to produce a valid argument for free will, you need to be able to either proffer a hypothesis for how such a "will-effect" chain can exist, or demonstrate physical transitions in a mind that are demonstrably not cause-effect or random byproducts of ordinary physics.
Even just come up with a coherent definition and you will be world famous, as you'd have introduced a new area of logic. If you can prove a physical mechanism for it, you'll have Nobel Prize in physics in the bag.
The main issue is that we approach the topic with a different set of axioms. E.g. your limitation of requiring a proof involving (a-c) is analogous to asking someone to build a steel bridge with three colors of legos.
Free will and consciousness are tautologically joined, so any attempt to create a framework to disprove/prove one or the other will have to be all encompassing.
It has the same issue though that you have to decide that you are conscious to begin using reason, even though no one can prove it scientifically.
If your starting point is that no one is actually conscious, it’s impossible to disprove, and it’s obviously wrong (and any attempt to prove it’s not obviously wrong would knee-cap itself since it’s impossible ‘to logic’ without a reasoning engine).
Well, yes. The alternative is for you to give me a definition of free will that allows for it within the constraints of cause-effect and randomness.
Without such a definition, the option we are left with is inherently "breaking free" of that, and then we need another category of effect.
I don't believe either is possible, but we specifically do not have evidence that such other category of "will-effect" transition is possible, no observed mechanism, no observation of such a category, nor a hypothesis that provides even the starts of a coherent definition of what it would even mean.
So yes, the point is that the problem appear obviously impossible to resolve in favour of free will without either new logic or a definition of free will I don't think possibly can meet expectations.
> Free will and consciousness are tautologically joined, so any attempt to create a framework to disprove/prove one or the other will have to be all encompassing.
Only partially, in the positive case. Consciousness would seem to need to exist for free will to exist, but in the event free will does not, there's no reason to presume that affects the possibility of consciousness.
> It has the same issue though that you have to decide that you are conscious to begin using reason, even though no one can prove it scientifically.
It does not have the same issue. Whether you have free will or not, there's no reason why that need to affect your life at all. Clearly we think we make choices. Whether we make those choices or not, we act as if we do. As it is, we already have solid evidence that our conscious "decision" often is not causally linked to the actual "choice", so we can't rely on our introspection to even give us an accurate description of what "choices" we make, or why, and we know from e.g. split brain experiments that the brain can easily be made to rationalise how it "chose" things it never did. Accordingly, whether the mechanism actually controlling actions exercise free will or not, we'd expect our consciousness to experience it the same way.
“Well, yes. The alternative is for you to give me a definition of free will that allows for it within the constraints of cause-effect and randomness.”
https://youtu.be/itLIM38k2r0?si=1wTeSVdX28UlB2jf
This interview with Nobel prize winning mathematical physicist Roger Penrose describes a framework where quantum mechanical time hopping during a measurement removes this cause-and-effect concern you have. E.g. The nature of reality of time and matter fields is even more complicated than we understand, and our macros scale understanding of cause and effects might be too limiting when considering constraints of consciousness.