Some of the wonderful things about the amateur radio community is that it is seamless, universally friendly, helpful, and well equiped.
There is a HUGE following of vintage tubed gear and the folks with the knowledge and tools to restore gear are EVERYWHERE, willing to help with access to a vintage tube tester (no longer found in every drugstore) and autotransformers. And scopes and signal generators for that matter.
Find your local amateur radio club, attend a meeting, request help on a tubed project and it will be answered.
@R Sweeney - Excellent advice, and when I said it probably still works I should have added the caveat about the electrolytics. Written in haste.....
Very few people have a variac or a tube tester to hand. A test of the disconnected electrolytics with a lab PSU at maybe 50V is a good start. If you're in the US you could then use an isolation transformer (a must) and a rectifier with a beefy 10K resistor in series to put about 160V on them, Leave it on for a bit , monitoring the current (should go quickly to a few mA or less), to let them reform. But caps of that age will usually be dry (= low cap) if nothing else.
If you can just replace the electrolytics (which is probably the best way to go) then you'd probably be fairly safe in trying a switch on, with a meter across the main electrolytics - if the voltage does not go up to a few hundred volts right away then switch off and dig further.
As a rebuilder of old tubed Heathkit ham gear, you NEVER just turn on the power and see what happens.
The 60 yr old paper caps on these pieces are almost 100% quaranteed bad, open or shorted. And those bad caps can damage irreplaceable components on failure, like hard to find transformers. And a surprising number of carbon resistors crack with age.
Step 0: get and read the manuals
step 1: replace the paper caps with modern high quality (non-Chinese) electrolytics
step 2: clean all the switches, pots, sockets
step 3: test the tubes
step 4: use a variac to SLOWLY bring up the line voltage to avoid in-rush issues with components which have not seen a magnetic or electric field for half a century.
step 5: if it works, rejoice, if not troubleshoot and find the dead guy(s).
step 6: Enjoy the rebirth of someone's old friend.
@Caleb: The surprising thing to me was when you took the cover off -- seeing how few components were used -- I was expecting it to be jam-packed with circuit boards and transistors -- I hadn;t realized it was vacuum-tube-based.
I am also circa late 50's and used this scope when I was a kid. For the younger crowd, an interesting aspect is the long neck of the CRT which is because scopes used electrostatic deflection rather than electromagnetic deflection. Faster, but a narrower deflection angle.