One of the things I remember a vastly experienced and distinguished editor saying to me was that you can't use semi-colons in dialogue. And although I'm normally allergic to "rules", this is one that I do pretty much stick to. And it's part of a larger question of punctuation in dialogue, vs. punctuation in narrative.

I think the point about semi-colons (which I love) in dialogue (where I almost never use them) makes more sense when you remember that punctuation has two completely different jobs: helping to express what a sentence means, and helping to express how a sentence sounds. Obviously there's an overlap, because how we say things is partly affected by the meaning of what we're saying, but sometimes the two functions are incompatible. And it depends what the writing is for, which of those two functions gets to dominate, and wins when there's a clash.

- In non-creative writing (for want of a better term), it's all about making the meaning clear: commas are about separating small units of meaning, colons about leading to extra information or explanation, and so on.

- In creative writing that's still true, but creative writing also, always, has a relationship with voice: with how things would be said as well as what it says. So sometimes we're using punctuation to get our text true to how-it-would-be-spoken, even if that means using it in ways which break the "rules" of how it works in its job of helping to express meaning. This is also why it's so important for a writer to internalise the rules of punctuation until you can feel them, as well as understand them, because when you're punctuating for expression, not just for meaning, you need to work with their feel.

- In dialogue, the how of what's said - the voice - is much more dominant than it is in your average narrative (though of course some of the best modern novels are very "voice-y"), and so punctuation is - well - y'know - likely to ... start to be - well, working in very un-rules-y ways, just as your grammar's likely to go kind of like wonky.

The main job of a semi-colon is basically the same as a full stop, except that, crucially, it explicitly makes a connection of meaning between two sentences which is closer than a full stop can make, for example in:
"John slept with the light on; he was afraid of the dark". But in terms of expression, any of us would pretty much say that sentence the same way whether there's a semi-colon or a full stop between on and he.

So, if the punctuation in dialogue is much more about how and less about meaning, then the semi-colon has no specific function; it tells us nothing about how the sentence sounds.

I can feel a blog post coming on... (And notice how this post keeps having to resort to laborious italics, as I try to evoke in text the important emphases which I could make so easily in speech.)

Very nicely put. I agree completely about the role of punctuation being twofold: on the one hand as almost mechanical coding devices, on the other as markers of timing.

I do think the semi-colon is in danger of extinction, whether in fiction or non-fiction; but not quite yet!

I think in the example you give, about John in the dark, there would be a slight difference in the way the two phrases were said, if they were two distinct sentences or separated only by a semi-colon. The semi-colon gives the reader the confidence that the next phrase follows in the same breath and there's no danger that the next sentence is introducing a very new idea that requires a slightly longer pause between the two phrases/clauses. So in general, in terms of the spoken quality of the text, the semi-colon creates a very slightly longer pause than a comma, but not as long as the pause of a full stop.

Clauses and pauses; pauses and clauses!

I read this and wondered if I ever did it. An hour or so later, I put a colon in a bit of dialogue. Did the vastly experienced editor hate colons, too, Emma?

Colon in dialogue ... hmm. If you put a colon in dialogue then you are still introducing an explanation, or a series, or a list? Is there another purpose? But if so, isn't that signalling (unfairly) to the reader what is to come? You're taking away the spontaneity, and the writer has to provide that list else render the colon invalid. 
I'm thinking of speech. When you are listening to someone you know when that person is going to start a list because of the tone of voice or a gesture. In writing, unless you include some guidance with the narrative the reader won't know what is coming in the dialogue. I think this is better.
No, I won't use them. Not in dialogue.

Interesting about the colons in dialogue. I suspect I wouldn't, because the difference, again, is more about the meaning than the sound. A sentence that might have a colon in it if it's written because it's the best way of conveying the meaning would in dialogue probably come out (or be re-shaped) to reflect the way we'd say that sentence if it's spoken.

For example, in narrative I might well write:

They went shopping with a list: cake, salad, fish and chips, and peas. Everything went according to plan; everything, that is, until they got back to the car.

but if a character said that kind of thing, it's much more likely to go:

"We went shopping and we bought what was on the list -  cake, salad, fish and chips, and peas - and it all went to plan. At least, it did till we got back to the car."

Mind you, if my dialogue is closely tied to how it would be spoken, my narrative is always very closely tied to how it would sound read aloud (not the same thing, but related.). Almost nothing, including tricky emails and CVs, leaves my hands without being read aloud. So they're still pretty close to each other, and down the "voice-y" end of the spectrum, perhaps.