Is Mythicism Falsifiable?

As Neil Godfrey helpfully drew attention to in a comment, there seems to be no agreement among Jesus-mythicists about when the earliest Christian sources were written, which sources are the earliest, or which ones are authentic.

This ought to raise suspicion that mythicism is a preordained conviction in search of any arguments that can be used to try to promote it, rather than a conclusion.

And so I thought it would be interesting to ask whether mythicism is falsifiable. Obviously if one could mind meld with ancient Gospel authors or time travel then in theory it might be. But in terms of the sorts of evidence that historians could ever find, is there any that you think would persuade a mythicist to change his or her mind?

And if not, does that not tell us something important about mythicism?