A lot of CRT's whine especially as they get older. It can be coils on the PCB, the flyback transformer, the windings on the yoke... often the glue/lacquer used on these components has broken down and is allowing them to vibrate.

One trick you can try to isolate the noise is take the cover off (being very careful not to touch anything!) , and hold a cardboard tube from a roll of paper towels up to your ear. Unfortunately there's no really quick fix, if you can find a local TV repair guy that still deals with CRT's they might be able to help.
I have a CRT TV with audible whine, but I draped curtains across it which pretty effectively deadens the sound.

Any recommended epoxy/goo formulations to use once the source is found?

Thanks for the advice. I've noticed that the monitor is totally silent when it's kept cool - if it gets hot (which it does when it's on for extended periods of time) it may begin to whine. It's also more likely to do it when it's running at 60 hz. This leads me to believe that it is in fact a winding somewhere - possibly the deflection yoke - expanding from the heat and resonating. Not a big deal, but it can get irritating. Thankfully, it was on for 3 hours before it even started to whine, so I think I'm good 😜