Started looking at U740 and I think I found some issue. This is pulse at TP5 as well as at CR751. 5MV/2ms and 5MV/1ms. That doesn't look right at all. Mostly ripple noise. Quick check of other pins of both U740 and U738 are showing same crap. I'm going to pick up in this area in the AM. It definitely looks fubar. Do you agree?
All stuff around that area, i.e. before c761/r761 does not depend on whether or not it is triggered; u780 is irrelevant.
u740 etc are classic long-tail pair differential amplifiers. The inputs are differential voltage inputs, the outputs are differential current outputs. If the input voltages are equal, the output currents should be equal. The output currents are converted into input voltages for the next IC by resistors, i.e. r731, r736, then r745, r746, r749 , then r751, r752 plus others around cr751. Using a single-ended scope probe can only measure the differential output current indirectly! The differential input voltage should be <100mV for linear operation; if it is more than 200mV the outputs will be fully saturated/off.
A good way to test that is to use the 1kHz cal out driving the external trig input (as per fig 6 top left). You should see a square wave on u740.5 and u740.9. At those two points I see unequal 200mV-800mV square waves, and the relative amplitude depends on the position of the trigger level control.
If you don't see those square waves, then start at u730.14, u730.16 (inputs) then u730.5, u730.9 (outputs), then u738, then u740.
I just scoped U740.5 and 9 with set to ext trig and the cal input and I see a square wave on each output. So that is working. However, varying the level control has no effect. You stated that it should change with the level control so should I go after that?
More info: U730.9 the amplitude changes somewhat with the level control. U730.5 does not change. U730.14 which is the input from the trig level control does change quite a bit.
If you have a square wave of sufficient amplitude at u740 outputs, that is sufficient to kick off the triggering. Any other effects would be second-order, and might be worth looking at when triggering is functional.
The next stage in this chain, before you get to u780, would be to look around the tunnel diodes.
Have you gone through the procedures to set the "a trig sens" "a arming" and "a output" trimpots?
Put a 10kHz sinewave into ch1 and adjust the vertical to have the trace around ~2.5 divisions peak-peak, trig from ch1. U738.5 should show a ~1Vp-p sinewave. If it is distorted by clipping then adjusting the level control should allow you to "recentre" it and let it be more or less symmetrical. Don't get too hung up about those levels; fiddle until it looks right, ideally when triggering is working correctly
Looking at the output of u740.5 will show a grossly distorted sine wave with significant clipping and worse. The key feature to look for is a sharp transition somewhere, which is the tunnel diode being non-linear. That's even more apparent on the other side of r752, where cr751 should be causing there to be a vertical gap in the waveform.
Skipping ahead, look at the junction of r762 r760. It should be a 300mVpp "square" waveform with sharp transitions, period related to the sweep duration. There should be four separate levels, three similar related to arming all the tunnel diodes, and one significantly different. The relative durations of those "phases" depends on the input frequency and the sweep duration. Personally I'd be pleasantly surprised if you saw that waveform, since it indicates everything is working!