Very often the best tube tester is the TV or radio itself. There's the "seven seconds off" test which is useful for showing up borderline weak tubes.
With the set running and warmed up, turn it off for about 7 seconds, and back on.
Is the width slow to fill out? That'd be a borderline Horiz out tube.
Vertical slow to fill out? Weak vert. out tube. Horiz sync slow to lock in? Hor. oscillator weak. Pic comes in snowy, then clears up? Weak RF amp tube in tuner. Etc.
Then there's the 'tap test' useful for showing intermittent tubes. Tap each tube gently with something like a screwdriver handle while watching the pic (use a mirror if necessary).
Intermittent heater-cathode shorts in the CRT often show up by tapping the neck.
Damper tubes are notorious for arcing, and will almost always respond to the tap test (no mirror necessary
).