I once had a friend who was at least at the sub-clinical level of narcissism (by my amateur reckoning of the matter). He was very clever, and got easily annoyed with people who thought were stupider than him, or who were wasting his time.
One of the things that manifested itself very strongly was that he was enormously sure of his own opinions. People who disagreed were nearly always morons, and were strongly mocked. This wasn't just on objective beliefs either - matters of taste, however arbitrary, were treated with similar absolutism. The gap between his taste and objective quality, in his mind, was zero. This would even occur when extreme positions were taken on otherwise similar issues. Because he was brilliant, his opinion on these matters must be right. He was also very funny, gregarious when he wanted to be, and and a keen reader of other people. I still count him as a friend, so don't get the wrong idea here.
So how do you tell that someone is narcissistic, rather than just stubborn and opinionated? There is, after all, substantial overlap. Do you fail to change your mind just because you believe things very strongly, or do you fail to change your mind because your belief in your own brilliance means that you simply can't contemplate the possibility of you being wrong?
One trait I observed was that when he did change his mind, he rarely acknowledged it for very long (if at all), and then proceeded to proselytize the new view with all the fervor previously given to the old. The self-image must be preserved at all costs. What you believe isn't strictly important. What's more important is that you're a clever, insightful person who makes good choices.
But that, to my mind, wasn't the key giveaway about narcissism.
The guy was a perfectionist in his job, and thus slow to actually complete projects. At some point, he didn't get promoted, and so was leaving the industry to work elsewhere.
Based on a hunch, I asked him at some point what things he had changed his mind on during his time in the job. I had suspected that it would be nothing at all, but that turned out not to be true.
He told me instead that when he started he had thought that good work would get rewarded, and the competent would rise to the top of the profession. But over time he saw that the senior ranks were just filled by rent-seeking people who had got themselves into positions of authority and expropriated smart, hard-working junior people.
Sensing that I might be on to something, I asked him to clarify something else. Had he learned or changed his mind on anything in a way that had caused him to update negatively about himself?
He paused, and considered the question for a few seconds, quite obviously for the first time. 'No', was his answer, which was the truthful one. He thought he was good, and didn't need to BS with false humility.
And I realised this was the crux of the issue. What he had learned, in other words, was that he was too good for the job he was in.
A narcissist can learn, and a narcissist can change their mind. But they can never change their mind in a way that causes them to update negatively about themselves.
If he had failed in the job, the problem must be the job.
And this also helped explain something else that I suspect is common to narcissists, and possibly to low empathy types who lean towards sociopathic behavior (I truthfully can't always distinguish these two cases cleanly, which shows that I'm not a psychiatrist, just an interested amateur - my friend I put mostly just in the narcissist category). Sophisticated narcissists who are low on empathy can be very good at reading other people, and using this to manipulate them. But every now and again, they'll also make spectacular own-goals in social situations that leave everyone else scratching their heads.
When I tallied up what caused these in the case of my friend, the one thing that he wasn't able to see clearly was what other people thought of him. He thought that everyone loved him, whereas a lot of people didn't. He could read people in general, and he could read what other people thought of themselves, but because his own image of himself was so dominant, it prevented him seeing what others thought of him.
I hereby volunteer as a job interview question 'what is something that you changed your mind on in a way that caused you to update negatively about yourself'. It's one that people won't have a canned answer for, and will tell you whether they're actually able to see their own weaknesses, or whether they lean towards narcissistic self-adulation.