So if I take some animal or some organ, check to see if anyone has found a plausible way that it could have evolved, and find out that, as far as I can determine, no one has done that, it would foolish to conclude that it must not have been produced by evolution.

Right. The absence of evidence of an evolutionary origin is not evidence of the absence of an evolutionary origin.

The point of that argument was this: The number of historical events is even larger than than the number of animals and organs in biology, so it will be even more true that many such events have had no good analysis by historians. So if I take one of these events and I don't see how it could have had historical causes, and I don't find any historians giving it a historical treatment, it would be foolish to conclude that it could not have had historical causes but must have had a supernatural cause.

Fair enough. Absence of evidence is not evidence of absence.

So, in short, you're suggesting that any claim of a divine origin for any historical event actually needs to be accompanied by at least some evidence suggesting a divine origin, and not merely a lack of evidence suggesting a mundane one?

That seems reasonable to me.