One good model of CRT tester is a Sencore CR70. There are many others out there, but be aware that a vintage tester may require the same sort of restoration as anything else that old.
A CRT tester may cost more than you paid for your TV. If you have a multimeter, you can at least test the filament to find out if your CRT is a total dud. This article explains how:
http://antiqueradio.org/FirstStepsInRestoration.htm
The rectifier tube in the HV cage is a 1-volt tube and you won't see it glow (if at all) unless the room is totally dark.
If you skim a couple of the TV restoration articles in this section, that should give you an idea what's generally required to make these old TVs work:
http://antiqueradio.org/restoration.htm
Be careful around high voltage, as noted many times in those articles.
I would not play the TV for extended periods until you have replaced (or at least checked) the electrolytic capacitors in the power supply.
Phil Nelson
Phil's Old Radios
http://antiqueradio.org/index.html