Just by giving a monitor a once over, what would make it clearly evident that there are problems with the tube itself?
no picture?
seriously, if there is a picture, and looking at the phosphor dots you can see that the green and blue are indeed lighting up (IE the other colors are operating too) you have a good start, and its usually easy to fix.
very likely: a shorted transistor causing the red to be turned on all the time.
likely: there is a badly adjusted pot
less likely: video amp chip issue
even less likely: shorted tube