The 'scope has been diagnosed and repaired. I'll briefly cover the main points-
The faults:
All the resistors in the voltage divider were open, including potentiometers.
Some (most) of the resistors in the intensity control circuit were open, others were out of range. These resistors are in an area on the horizontal board where a red, and a white with red trace wire are connected, rear R/H corner, and cover an area about the size of a matchbox.
The high voltage was chronically low in some circuits, but not others. This was quite a mystery until a sneaky 0.02uF 1500 volt capacitor linking cathode (CRT pin 3) to the external cathode input terminal was checked. Follow the yellow cloth covered wire. This capacitor is in the area for the voltage multiplier, under the socket end of the CRT and directly behind the banana sockets on the rear.
The resistor from cathode input to ground was shorted. This was at first thought to be the shorting link, but tested faulty when disconnected.
There is a 200K ohm resistor inside a transparent sleeve that is connected to the centre leg of the front panel intensity pot, alongside a white with red trace cloth covered wire. I would strongly suggest testing this resistor as well. All the failed resistors were in high voltage areas, and this resistor is as well.
Schematics will be posted on the web soon. As soon as I have the U.R.L. I will publish here.
Once all the faults were attended to, a trace appeared. Wobbly at first, but over time has settled down to a nice crisp straight line.
Thanks to all those who constructively commented on this subject. Learning the basics of diagnosis has been one steep, but very enjoyable learning curve.
Regards,
Clay.
P.s.
If you are inexperienced around high voltage, be very, very careful. I blinked at the wrong moment, and I'm up for a new DMM.