Iirc these tubes are a hell to service/adjust - you need proper gear and knowledge.
(and it's dangerous for mechanical and electrical reasons, as you probably know)
At least I can assure you that back in the days we exchanged
all such tubes with replacement parts.
Not even the guy with full TV service education would touch them.
If you used your iMac on a regular base it may well be just the natural wear out.
Best approach would be to pick one from trash/private sale that spent most of it's time on attic and exchange the tube (if you cant't part for emotional reasons)
Assembly isn't too complicated, but if you remove the high voltage cable from the tube be extremely careful: the inside of the tube keeps a 20kV load for a very long time.
You may also consider that burning tube circuitry may permanently pollute your home with dioxin, when the thing may blow up due to age.
I'd rather switch to a G3 B/W, which is very affordable and at least kind of similiar in style.
Turn the oldie into an aquarium or something similiar