The fitting needed about ¼ turn to tighten it and the smaller nut about ⅛ turn. Switched back on and nothing on the cold dental mirror. The left rear corner also scarcely warm now. Left on with the top cover on while we go out for lunch. Optimistic that all will be well. The glass on the gauges also looks pretty clean now so maybe nothing needed to be done there.
Thanks again for all suggestions and advice.
If it happens to the one in France I should be able to fix it easily.
I might just check and tighten the fitting anyway as a pre-emptive precaution as it’s pretty easy to do.
I used a 19mm socket which, after removing the connector, was easier than the awkward method with an open spanner on the Lelit video. The socket wasn’t quite deep enough but if dropped onto the fitting the extension sat just far enough in to hold well enough.