In a nutshell, I'm wondering how far one can parse things with accusations of logical fallacies before it becomes absurd.

I'm thinking specifically of a discussion I had with a supporter of Donald Trump... I had provided two articles with several reputable psychiatrists, psychologists, and social workers who had all raised concerns about Trump's narcissism, to which I was accused of an "Appeal to Authority" fallacy because the supposed authorities did not follow prescribed DSM protocols, and that Trump had thus not been formally diagnosed as narcissistic. Granted, the psychologists in question may have breached professional ethics by breaking the "Goldwater Rule," but, it seems to me their training and, to me obvious authority in the field, lends a degree of credence to their assessments and concern over Trump's candidacy for President of the U.S. There is an inherent paradox here, since Trump would likely never submit to a formal assessment, let alone allow the results to be made public. So, all we are left with is conjecture and speculation albeit from very high authorities. Isn't that enough to arrive at an error-free judgment on the matter? Or is this a case where one just has to accept that the absolute truth may never be known?

Basically anybody can call "fallacy" since informal fallacies are subjective and have quite a bit of wiggle room. It becomes a matter of who has the better argument: the one with the accusation of the fallacy, or the one attempting to demonstrate why it is not a fallacy.

As for your specific example, I would like to see how you worded your claim or argument. If you simply provided the examples and said that you were concerned about his narcissism, it would be difficult to find any fallacy in your opinion. However, if you claimed that Trump was clinically diagnosed with Narcissistic Personality Disorder, you would have to argue what it means to be "clinically diagnosed."

I would not agree that this is an appeal to authority because a) the authorities quoted were relevant authorities on the issue at hand and b) their views are not outliers given all the proper authorities who have views on the issue. I am assuming here that as you said, concerns were raised about narcissism, not that he has Narcissistic Personality Disorder (we all have some level of narcissism).

Expressing my opinion here (outside the question of fallacies), I am not a licensed clinical psychologist so I cannot speak authoritatively to Trump's suspected narcissism, but I can say that such a disorder manifests within a certain environment. Trump, like most CEOs, can use his narcissistic qualities to his advantage in business, making the characteristics more adaptive than maladaptaive. However, once in an different environment, like being President of the USA where he represents the people of American, is integral to diplomatic relations, and has the nuclear launch codes, these narcissistic tendencies can become hugely problematic. UUUuge.

Beyond the obvious fact that, as you acknowledge, Trump hasn’t been clinically examined by these psychiatrists (and this alone renders any ‘clinical’ diagnoses completely specious) one may reasonably speculate whether there would be unanimity of psychiatric opinion, were he to agree to be examined by several. I suspect the degree of egregious narcissism uncovered would be inversely proportional to practitioners’ affinity toward Republican viewpoints & thinking.