Having now had a look at the laptop itself, I'm afraid I still can't add anything useful to the discussion. The red line has simply disappeared, apparently of its own accord, and the display now seems entirely normal and stable.
I've tried a little 'bench treatment' (i.e. giving the thing a sharp nudge or two in the hope of showing up a loose connector) but I haven't been able to reproduce the red line. So I propose to leave well enough alone and get on with the rest of my holiday.
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