To place your rationale to rest, no, I cannot prove that Julius Caesar is real, anymore than I can prove Jesus the Christ was real

But I gather you are picking up what I'm putting down...
My point is that the conclusion that Julius Caesar existed is the result of sound reasoning, but is not falsifiable. Historical facts and scientific facts work differently, but this doesn't make all historical reasoning a matter of logical fallacies.
In other words, you are abusing the term "logical fallacy" in defense of a problematic theory of justification of knowledge. Empirical testing is not a requirement outside of the natural sciences, and even there, falsification is not an entirely uncontroversial notion. Some of those string theorists certainly attack it.
Demonstrate a logical case for the existence of an asserted 'causal agency', without violation of a logical fallacy. If (you) cannot, then I guess we can both bask in the plausible 'argument from ignorance fallacy' ourselves
I'm going to start with the wikipedia definitions of the three types of reasoning:
Abductive reasoning (also called abduction, abductive inference, or retroduction) is a form of logical inference which starts with an observation or set of observations then seeks to find the simplest and most likely explanation for the observations.
Deductive reasoning, also deductive logic, logical deduction is the process of reasoning from one or more statements (premises) to reach a logically certain conclusion. Deductive reasoning goes in the same direction as that of the conditionals, and links premises with conclusions.
Inductive reasoning is a method of reasoning in which the premises are viewed as supplying some evidence for the truth of the conclusion (in contrast to deductive reasoning). While the conclusion of a deductive argument is certain, the truth of the conclusion of an inductive argument may be probable, based upon the evidence given.
Here is what you do not understand: an argument from ignorance is automatically an
abductive inference. It involves a sort of attempted inference to the best explanation, which makes it fairly tricky to determine where the line between legitimate and illegitimate abductive reasoning might lie. Much if not all of empirical science is based upon abductive reasoning, so the degree to which you are disparaging abduction here while championing empiricism is actually fairly intriguing--the ability to test an abductive inference doesn't determine whether or not it is fallacious, just whether it is
scientific. I'm honestly not a fan of abductive theistic arguments myself, though I don't think it's fair to label them arguments from ignorance simply on account of being abductive.
Abductive reasoning is not the only type of reasoning, however, and not the only thing you will find in theistic arguments, though it is admittedly more common these days. Still, deductive and inductive versions of cosmological, teleological, and ontological arguments exist as well (see Aquinas for the first two, and perhaps Gödel for an interesting modern ontological argument). None of these are going to be arguments from ignorance because
they're not abductive in the first place.