A common way of characterizing the fallacy is along these lines:
Statement p is unproved.
Therefore Not-p is true.
Statement not-p is unproved.
p is true.
But it's hard to see why this is fallacious; it is natural to read it as both defeasible and enthymematic. Walton, among others, has noted that as a matter of practical reasoning, this is often an excellent form of reasoning. (I have not determined that this gun is unloaded; it is reasonable to regard it as, for all practical purposes, a loaded gun unless it is shown to be otherwise.) But practical reasoning leaks into speculative inquiry; and as a purely speculative matter the above forms of reasoning can be quite reasonable. If I say, "There is no evidence that such-and-such drug has the effects attributed to it," I am not appealing to ignorance. I am appealing to the evidence of the inquiries themselves, the inquiries that have been made into the effects of the drug in question, and it stands or falls with the adequacy of these inquiries. Copi, in a typical hand-waving maneuver, tries to block this by saying that in such cases the argument is really based not on ignorance but on our knowledge that if the matter were to occur (e.g., if the drug were to have the effects attributed to it) it would be known. But this would save any supposed appeal to ignorance from being considered a fallacy. For surely they can all be interpreted as making the assumption that if p or not-p were true, this would be known or proven. Put them in the form of a modus tollens:
If p, it is proven.
It is unproven.
If not-p, it is proven.
It is unproven.
Thus the bar is so high that it seems absurd even to charge someone with the fallacy unless you have truly excellent reason to think they are basing their argument merely on a claim of general ignorance and nothing else, not even the assumption that we would discover it if it were true. But when are we ever going to encounter such an argument?
The Wikipedia article on the fallacy is about as close to perfectly incoherent as it could be. At one point it would seem to require us to say that every scientific conclusion commits the fallacy. For instance, it gives this as a nineteenth century instance:
The solar system must be younger than a million years because even if the sun was made of solid coal and oxygen it would have burned up within that time at the rate it generates heat.
Exactly where this example is from, I do not know. But on the suppositions presented in the article, this is an entirely reasonable argument that commits no fallacy; it provides a scientific reason for arriving at a conclusion, and one that was decent enough at the time. It errs in its assumptions about the nature of the sun, of course; but it doesn't appeal to ignorance in any way, shape, or form. Something doesn't count as an appeal to ignorance simply because there might be new evidence that could not have been pointed to as evidence at the time.
Walton points out, in an excellent discussion that the first classification of arguments that includes argumentum ad ignorantiam is given by Locke. It is one of "four sorts of arguments that men, in their reasonings with others, do ordinarily make use of to prevail on their assent; or at least so to awe them, as to silence their opposition." But Locke's argumentum ad ignorantiam is simply an argument by challenge: I argue that you should either accept my proof or provide a better one. As Locke notes, this argument does not advance us in knowledge, since knowledge can only come from "the nature of things themselves," not from my relative inability to avoid being outargued. But it does not follow from any of this that it is a fallacy, and Locke himself does not claim that it is. Locke's argumentum ad ignorantiam is inferior to the one form of argument that serves as a way to get knowledge, the argumentum ad iudicium, because it appeals to the interlocutor's ignorance (since you can't think of a better way than mine, shut up) rather than to his judgment. It shares this inferiority with the other two kinds of argument that don't tend toward knowledge, the argumentum ad verecundiam (which appeals to the interlocutor's modesty with regard to authority) and the argumentum ad hominem (which appeals to the interlocutor's own concessions). But it is not fallacious to appeal to experts (which is clearly a form of what Locke calls argumentum ad verecundiam), nor is it fallacious to show that if your opponent were consistent in his claims that he would agree with you (which is what Locke calls argumentum ad hominem); likewise, neither is it fallacious to appeal to the interlocutor's inability to have a better position than yours. It just doesn't give you "the nature of things themselves."
Walton always seems to assume that what Locke is describing is what later people would describe as the argumentum ad ignorantiam. It's not clear to me that this is so. Locke, I would suggest, is really talking about persuasion. His four sorts of argument are really four modes of rational debate, four ways in which you can persuade someone to assent to a position: by appealing to authorities and experts whose views they would or should respect (ad verecundiam), by pointing out their inability to argue for a better one (ad ignorantiam), by showing that what they have already conceded or would be willing to concede implies that position if they are to be consistent (ad hominem), and by giving them some direct evidence of the way things really are (ad iudicium). We all use these very often, and for good reason; they are essential parts of rational rhetoric, i.e., the rational means of persuading others. A longstanding attempt to salvage the notion of argumentum ad ignorantiam to see it as a fallacy of shifting the burden of proof. This clearly has the merits of both conveying something like what we usually mean by it and also conveying something like what Locke means by it. But it requires a very particular and very controvertible view of burden of proof even to hold that there are any fallacies related to burden of proof.
Leibniz had already pointed out in response to Locke's characterization of argumentum ad ignorantiam that there are cases where it is reasonable to accept a position until its contrary is proven. Whately, interestingly, claims in Elements of Logic that argumentum ad ignorantiam just means arguing with some kind of fallacy with an intent to deceive, and is therefore not a specific kind of fallacy at all. (Many informal fallacies are understood by Whately as only fallacious if there is an intent to deceive by substituting a not strictly relevant conclusion for the relevant one.) The same idea is found in Stock's Deductive Logic.
Which raises the interesting question of who started the use of phrase for arguments of the sort we usually mean by them. I find an obscure statement in McCosh's The Laws of Discursive Thought (1873) that the fallacy involves insisting that someone believe something "because he knows nothing to the contrary". He gives the right sort of examples, too: clairvoyance, animal magnetism, the cons of priests and pretenders, etc. But even earlier, William Dexter Wilson, in An Elementary Treatise of Logic (1856) says it "consists in proving that a given Proposition is true, because we know of no reason why it should not be true, or why the truth should be otherwise". His discussion has all the incoherence of modern discussions too: it's a fallacy, but not always, and the sort of reasoning is bad, except when it is not. (He does do better than Copi, however, in recognizing that cases of argumentum ad ignorantiam pretty standardly involve the assumption that if p were true we would or could know it.)
Of course, I think the 'God of the gaps' charge is often quite reasonable. I don't think it is so when it is understood as claiming that the argument commits argumentum ad ignorantiam. Rather, saying that an argument is a 'God of the gaps' argument involves saying that (1) there is a gap requiring some causal or explanatory factor; (2) God is posited as directly fulfilling the role of that explanatory factor; but (3) we have reason that we do not need, or in the end will not need, to posit God in this role at all. It's a claim that the argument is hasty, jumping to conclusions, by attributing something directly to divine intervention that we have reason to believe is directly attributable to natural causes, even if we are still in the process of determining exactly what they are. Understood this way, it has nothing whatsoever to do with the fallacy of appeal to ignorance, being a claim about the best way to go about filling the gap. Thus I do think Larmer is on the right track in suggesting that it is really about whether the conditions for a good search-based inquiry have been fulfilled.