I think that as soon as one defines free will, it can immediately be refuted.
This is clearly (at least trivially) false. Define free will to be that which is true. Then it is. Of course, then it's useless and meaningless, but the point is to be as careful as is possible with definitions. I've defined free will several times here over the years. You're welcome to immediately refute these.
The problem is that it is left vague and illusive
Not only are words polysemous, but most linguistic units aren't words but constructions.
I believe in determinism, which leaves no room for any way that an agent can think/want/decide independent of antecedent conditions.
It also contradicts quantum physics and leads to paradoxes in the general theory of relativity. Is your belief dogma, religion, ignorance, or a sophisticated interpretation of modern physics the nuances of which resolve the apparently obvious indeterminacy of physics?
There is no way to isolate the mechanism where an agent's choices are independent from the laws of physics acting on antecedent conditions.
That's true (IMO). And if 'free will" is understood to mean the capacity to act or decide utterly without external influence then this would matter. I know of no serious scientists, philosophers, nor fields in metaphysics or philosophy which understands free will as such.
To convince me that free will exists, one would have to point to a mechanism or step in the chain of cause and effect where a choice is not directly caused.
I've referred to several studies in this tread alone which do so. Quantum mechanics has entailed such phenomena since EPR and Bell provide a rigorous test in the 60s, but it wasn't until the 80s that actual experiments demonstrated in multiple ways that the determinism you espouse is a 19th century relic. That's without getting into systems sciences and complex systems.
Sometimes people grasp onto the uncertainty of quantum physics
They do indeed. And they are often refuted by those who know even less about modern physics relying on equally nonsensical arguments.
, but all that does is enter an element of randomness into the equation
No, it doesn't and can't and a passing familiarity with QM would reveal so.