Is it good English to say "They have just left", when talking about a single person (perhaps someone you don't know the gender of)?
(I am a native English speaker, I'm looking for the view held by lexicographers).
Singular they has been used in English for a long, long time. Seriously, Shakespeare even used it.
Unfortunately, a significant number of English speakers think it's wrong. Why? No clue. I'd label it a hypercorrection.
I think the most important thing to think about is whether your audience will understand you. On this count, singular they really shines, as everybody — even those who pooh-pooh it — understand exactly what you're saying.
Another consideration is what alternatives you have. One sounds stuffy; he or she is too long; just he is inaccurate (and possibly offensive).
Singular they is really the best way to go.
When using the plural third-person pronoun to refer to a single person, grammatically you are introducing a disagreement in number. So this is technically an incorrect usage and, again technically (and historically), one is "supposed" to use the third-person singular masculine pronoun he where gender is non-specific.
All that is changing. Since the advent of the women's movement and feminism, people have felt uncomfortable substituting a masculine pronoun in such cases, as if women were some lesser beings wholly submerged by men. This led to some difficulties. It makes for painstaking sentences to always refer to "he or she" when you don't know the gender, as in
That's fine for a simple sentence, but if you get into a paragraph where you constantly have to use "he or she" to refer to the subject of the paragraph, it makes for some tortured writing.
Informally people use "they" all the time to avoid this kind of thing. There was an effort some years ago to introduce a neuter set of pronouns ('tey', 'ter', 'tem'), but like all such manufactured language solutions it was destined to fail. Just because something may be a good idea doesn't mean anyone will actually use it.
I even find myself writing "someone ... they" and having to go back and edit. If someone uses it as you did, saying "They just left" to mean someone just left, I wouldn't worry about it at all.
It's considered wrong by some people and generally avoided by most, but I think it's going to become standard in the future as there aren't any other attractive alternatives and as non-traditional gender identification becomes more accepted and common, we will find ourselves needing such a pronoun more often.
The following quotes are from the wikipedia article. It seems to me that they all use "they" for generic person. For example, in the Chesterfield's example: "If a person is born of a . . . gloomy temper . . . they cannot help it.", "a person" appears to be singular but it represents any person. It is essentially plural.
'Tis meet that some more audience than a mother, since nature makes them partial, should o'erhear the speech."— Shakespeare, Hamlet (1599);
"If a person is born of a . . . gloomy temper . . . they cannot help it."— Chesterfield, Letter to his son (1759);
"Now nobody does anything well that they cannot help doing"— Ruskin, The Crown of Wild Olive (1866); "Nobody in their senses would give sixpence on the strength of a promissory note of the kind."— Bagehot, The Liberal Magazine (1910);
"I would have every body marry if they can do it properly."— Austen, Mansfield Park (1814);
Caesar: "No, Cleopatra. No man goes to battle to be killed." Cleopatra: "But they do get killed" —Shaw, Caesar and Cleopatra (1901);
"A person can't help their birth."— W. M. Thackeray, Vanity Fair (1848);
"When in the Course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another . . ." —United States Declaration of Independence;
On the other hand, I think the use of singular they in the following example is grammatically incorrect because it refers to a specific person hence it is essentially singular.
Someone was approaching my room. I could see that they were alone judging from their footsteps. They knocked on my door. I didn't answer. They knocked again. I still didn't answer so they left.