My approach has been influenced by all of my interactions with conspiracy theorists in the past. One thing I try to avoid is what I have called the “conspiracy theory pattern”. It goes like this: First, I find some evidence that refutes one of the theory’s supporting facts, next, the defender of the theory essentially avoids the evidence I presented and then brings up several (usually more than five) other facts that supposedly also support the theory.
This has the effect of keeping the overall theory protected since the issue in question doesn’t get resolved - rather, the theory seems to get even stronger as all of these other supporting (but thus far not proven) “facts” are brought up.
In my experience, it turns out that those other “facts” usually end up being a large pile of debunkable (is that a word?) “maybes”. It’s as though protecting the theory is more important than uncovering the truth - as if they have such a strongly held belief that their theory is true that they refuse to let any of the supporting “facts” be debunked because any debunked “fact” threatens whatever vested interest they may have in the theory being true.
They might also twist a fact into a pretzel shape so that it can fit into their theory. Of course I have found that this happens to most people defending their theories and so this behavior is not necessarily proof of anything, it’s just something to keep in mind as we go through this. My idea is that once all of the facts are proven true or false individually, then and only then can the true ones be gathered together to form a theory.