A valuable piece of test equipment

Other pieces are just as important too!
(Edit) 11-28-2020
Test equipment
Audio Generator
Battery Tester
resistance and capacitor substitution Box(s)
Signal Tracer
Transistor and Crystal diode tester
I consider anything that has an influence on testing as a piece of test equipment.
My list would include a: (not in a particular order)
Signal Tracer
Multi meter and probes
Volt-ohm-milliameter (20,000 ohms per volt)
Variac
Isolation transformer
Dim Bulb tester
Signal Generator
Soldering Iron (it's a tool)
Power Supply with connectors and leads
Oscilloscope and probes
And of course Manuals of Schematics
Work Bench or table
Hand tools
Wire
Solder-Solder wick-Solder extractor
Manuals for the test equipment
And above all Else a Light and Radio to listen to.
Then there are storage shelves
Hardware parts bins (Akro Type)
Least if not last Electronics Knowledge - Schooling - Math - Theory

Make a list and Keep records of everything you have Preferably on Computer with a spreadsheet and Database.
Hint Vacuum Tube Voltmeters that are subject to damage from rough handling or use are delicate and need to be protected. The solution is to wire a toggle switch in parallel to the meter posts and flip it to the on position to short out the meter movement, because it will dampen the coil. The when you use it flip the switch to the off position.

Note:  Using a bare wire on meter movement posts will do the same protection. Of course remove the wire before using.

I would say a signal tracer.
Why?
 Well, it does depend on what you are servicing.
 For me it was radios and other consumer electronics sets. 
I found it indispensable for any audio gear. Radios, tape recorders, amps, etc.
  I have an old Eico I modded. By connecting the RF input to the audio input I can now listen to the output of a tape head!
 I did up the voltage on the blocking cap to 1600V.

Often I don't even need to look for a tube pinout.
Really loud buzz if an a.c. fil wire, a milder buss at 120 cy. is B+ quite often, and it is easy to find the input grid and plate pins too.

Now there are many articles on how to build a tracer. Solid state or tube. Personally, I would use tube, only because of the fact that most of the solid state tracers won't handle tube voltages you find in a radio or TV set.
 

You can even make one out of an AA5, PROVIDING it has a TRANSFORMER for the power supply.  Also replace the AC isolation caps to ground before using. 

If it is not isolated, and you use it, you will at the very least cause sparks and possibly electrocute yourself.  NEVER, NEVER use an ac/dc set. No isolation. 

 ALWAYS use an isolation transformer on your test equipment and on the equipment under test. 
  Make sure the isolation transformer or the socket on it is NOT connected to powerline ground.
 If it is connected to powerline ground, BAD THINGS CAN HAPPEN. SOMETIMES FATAL!


 Just add a switching input jack to the radio and feed your signal into the grid of the first audio tube.

But you say "I am working on a TV set, how can this help me?"
 Well, you have an audio stage, right? Ok there you go.

"But I want to trace tuner, IF, Vert & Horiz signals".

OK. (Entering Mad Scientist Mode) 
Take an old transformer powered TV set and add input and output test points and a switch to where you want them. A schematic is likely a necessity.
 There were several articles on this in the hobbyist magazines a few score of years back.
 They were for B&W sets and color sets.
 You think you have a tuner problem? Run the tuner of the test Tv set output to the tuner input of the TV you are working on.

No Vertical? Feed the input or output of the vert amp in the test TV into your set under test.  Easy to find your section that has failed. 
 Now I don't recommend this sort of TV test jig for beginners.
 You will need to know what you are doing.

As always, I take no responsibility for use or misuse of the above information. I am not your mommy or keeper.