No. This is very typical for a broken solder point or a marginal
connector. This is also very hard to find. Fix is easy once
you know here the problem is. If is a connector, you may
want to remove and reseat every connector you can get at. Be
careful that the CRT may remain charged up to some hours
after it has been disconnected from power.

Thanks for the quick reply. I did look to see if there would be any
obvious stress from the case being on, but you're right it is probably
going to be hard to find and somewhere *not* obvious.

You now have to decide whether you want to systematically resolder "all" the
joints, rather than trying to find the specific bad connection.