Personally, David, I don’t like the use of a semi-colon. I’ve read articles about how it’s use is dying out or even some which suggest we should just get rid of it. Periods, exclamation point, question mark, ellipsis, double-dash, I think that’s pretty much all we need in the way of punctuation relative to dialogue.
As far as “beep… beep… beep…” is concerned, again, no rule. You could write it like this.
Beep. Beep. Beep.
Beep, beep, beep.
I’m not sure any of them convey something different to a reader. I suppose a writer may think the ellipses suggest a longer space between beeps.
As noted in the OP, as long as what you do doesn’t detract from the read, you can pretty much do what you want.