The fault is probably in the blanking stage, where the CRT control Cathode pin is not being turned off... if no other problem exists however; although it also sounds like the EHT to final anode CRT is not discharging, regarding your PSST or even Hiss sound.
First of all, with no power supply connected; take a test lead and crock-clip one end to the chassis, the other end connect a 1K resistor... then probe the CRT final anode for 5 seconds, and all the other CRT base pins, for any residual high voltage; then do your inspection and metering for continuity.
Do a simple look around the CRT earthing, it's outer screen first, if there is one... so it has a good earth connection to the chassis; then check the CRT base connections too, that they are in good electrical condition, by pulling off the base connector, and see if their is no oxidation or signs of green/copper oxide around the pins, even check for good solder connections at the CRT tag pins too.
It's also worth checking any deflection PCB's if they have plug-in edge connections, pull-out and clean !
Other than that, it's down to electronic fault tracing, good luck.