Has anyone else seen this? I have a quad of EL84's and when I power the amp on, one of them glows really bright, then the others come on and that one's glow dies back down. ...
I have certainly seen this on 12AX7s ... I have this one 12AX7, a old Mullard that goes positively 100 watt incandescent lightbulb bright when first turned on. It's fairly alarming. ...
I've seen it a bunch of times. Generally happens in certain era tubes from the Philips conglomerate (Mullard, Philips, Amperex, etc.)
Is this is a sign of something amiss with the tube, or just a weird anomaly? I've never seen this before.
Perfectly normal for these particular tubes. Bottom line, something about the heater's metallurgy in a series of tubes from Philips during a particular era caused them to emit a lot of (pretty bright white) light when they are cold and you switch them on. As they heat up, the light dies down pretty quickly. The particular tubes which do this will always do this, and it won't shorten their life. I've got quite a few Amperex and Mullard tubes which do it, and like Eleventeen said, most are preamp tubes.
I'm not terribly surprised that you might encounter it in an EL84, but I would expect EL34's to exhibit the behavior. That said, the visible portion of the heater and the position of the getter flash are such you might not see a flash which did occur.
Enjoy the tubes and don't worry. They're fine.