I don't find the circuit diagram easy to follow. I think pin 3 of the CRT (pin 5 on P303) is the first grid of the CRT and should be several volts negative to the cathode for normal operation, just like with a vacuum tube. Possibly at -10V it totally cuts off the beam and at -5 it's as bright as it should be. The brightness control and flyback blanking affect the voltage on that grid.
As a hunch I'd change R346, a 22M resistor, for a suitable high voltage replacement.
If your luck's out, you have an internal disconnection between pin 3 on the CRT and the grid. You should still see the voltage on pin 3 change, with respect to the cathode, when the brightness is adjusted.
You could measure the voltages, and with a codge force pin 3 to be say, 18V negative to the cathode. That should at least dim the display.
I'm sure I don't need to tell you that oscilloscopes can bite, so be extra careful.
I told you, I spent many hours on that scope .....
Consider it an investment of time rather than an expenditure, and all part of the joy of learning.