A few more high-rez pictures to show the wiring would be good, to finalize a schematic.
If you can mention any text on part values i.e. kV, pF, ohms etc and on the panel meters, that would be good I'll add it in.
I suggest adding a jumper wire across the two HV binding posts or across the (can) filter capacitor, as there is a little hazard.
This is probably what the dangling white wire is for. I would carefully short the cap and then connect the other end to that screw terminal.
Older high voltage oil-filled capacitors are stored and shipped with shorting jumpers across them. I was told this is to prevent them from accumulating stray (static) charge, which can bite (and from dielectric absorption, but this has not been powered up for a very long time, so not a concern). Modern caps (i.e. microwave oven) have a built in bleeder resistor to prevent this- but not in the 1950's.
I think this VTTC was to be a push-pull design but stayed wired-up at lower power as a single-ended circuit, probably to optimize things.
I would say it is built from scrap parts from a high power radio transmitter.