[Opcom]

TK-1 update: I have had the TK-1 and 2F21 CRT now for some time. Sorry for the very slow updating, but there are definite prerequisites before proceeding to the next step of troubleshooting and a repair.

Just recently, was kindly provided the manual for the WP-33 low voltage (main) power supply. That's important because the power supply will have to be duplicated from a performance standpoint to get the precise voltage regulation required at the TK-1, which is on the order of that from a laboratory power supply.
The WP-33 supplies all of the circuits for H and V deflection, oscillators, in/out, and video signal processing, as well as a 3 Volt DC source for centering the raster via yokel connection.

Also got a replacement HV transformer for the 2F21 circuit itself, as that and other things are missing from the TK-1 chassis, and there was some butchery of the high voltage section in the TK-1, perhaps a last ditch attempt to keep it running or resurrect it?

The HV power transformer for the CRT was/is known anecdotally as a 'weak point' on that chassis. A TV museum a few hours away has a TK-1 in working order and has had to make up their own HV supply using an oscilloscope transformer. That is a good solution and I assume their HV is regulated.
Despite finding a good transformer, I have to find the root cause and go from there to prevent the original problem if at all possible.
This transformer and its rectifier and filter produces a DC voltage of around 1800V which requires very close regulation so that its output is not modulated by line-voltage fluctuations and other minor disturbances like CRT current, lest the scan dimensions on the target plate change.