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HM307.
Your picture showing the return trace on posting#82 shows the classic fault condition for failed blanking.
These transistors seem to fail frequently. T352 is failed from your voltage tests. Any switching PNP will do, rated >50v. The 40v rating of your BF440 does not leave much margin for surges.
If your junk box doesn't provide and you have to get a replacement, I would replace both the PNP BF440 and NPN BF199. These are german types.You might find cheaper generic types like 2N3906/2N3904. Your BC327 is fine for the PNP. Try changing the NPN as well. Then look to the Opto coupler.

As WaveyDipole says, you can always try out almost any generally suitable transistors, on the basis that if it gets the thing working, then you can go on to any other faults. You can always go back later to optimise performance.
In this circuit, a replacement transistor which is not switching fast enough would give a smear at the beginning of the return trace on the highest TB speed. You can often live with minor points like that anyway.

As I suggested a long time ago, stop the timebase operating to measure voltages.
The trace will then be blanked. Then switch to External X and the trace will change to full brightness. That should be self evident.
If the optical coupler is failed, IC304, look for a change of 3v at the input R363 when you move the switch. If OK, go to the high voltage points at output of the IC p4 and then the collector of the driver transistor T353.
If you leave the timebase running, with blanking that is a switched pulse, the voltage you read on a meter will depend upon the mark-space ratio of the timebase sweep to flyback, so could be anything.
At worst, use the slowest TB speed, as then an analogue meter will have time to respond and will judder between the two voltages. A digital meter will get confused and just flicker away.

I agree with WaveyDipole over the 100V. May well be the tolerance on the zener Z351. Wind the two set brilliance range presets R356 and R357 to furthest apart, so that the range on the Intesnsity control is greatest.
You have about 100v across Z351 zener. so OK, and the -875V looks right enough, but should change. Reading of 875 suggests T352 driver is hard on. Either the diode D351 has failed, or there is no blanking pulse coming from the Opto coupler.
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