See if the Cherry microswitch is is opening and closing. That will do what you describe if it is not mounted right. This is pushed by the pin on the front knobs. The white spool is between the pin and switch. This plastic piece looks like a spool or bobbin used in the underside of the area where the needle goes down into is on a sewing machine. The main time knob that pulls out activates this switch. I have seen this problem before. The two screws that are on the readout board attached to the switch on the small metal plate adjust the switch physically.
Check AR like Dan G. said. His advice is the best place to start signal tracing. That AR point is T.P. waveform 8 which shows 6V peaks. This point is the extreme lower left of the board. A 51 ohm resistor is going to that test point. If no signal there, go back to test points in the hexagon numbers to see where you have it. See if TP550 waveform is there. That you can solder a short piece of wire at the base of the TP and bend it out towards the front to access it with a probe. At least the board can stay screwed back on for further testing. Remove the wire after the problem is found.
At point AF above P801 should be about .8V peaks according to number 11 waveform on <4> which is also waveform 9 on <5>
Are the pulses coming in on pin 1 of U820? It should be about 450mV peaks.
I am assuming the contacts on things have been cleaned and known working. If not, clean them. The three switches below the time knobs are frequently dirty being open on the end allowing dirt in.
The voltages on the triggering boards can be off. Depending upon the S/N of yours, check the voltages at points were internal adjustments are to see if any are off. Int. DC Bal and/or Sens pots could have been turned by the previous owner.
If your S/N is below 70000 then the tunnel diodes are the most likely cause of no triggering. Checking waveforms at the test points 7 on <2> or at pin 1 of U820 (waveform 8) will be a good indication of the tunnel diodes operation.
Another thing I have seen is the solder connections of these stiff gold pins not be adequate. It is possible one or more of these need additional solder. The ones that I have seen bad this way are usually the ones where the trace is on one side of the board and the solder for the pin is on the other side of the board. The ones that have this problem, I added a bit of solder at the base connecting it to the trace. This plug-in is one I have seen this on where the logic board is connected to the main board.
Check the other transistors that are 3571TP. You will find the Q numbers in the parts list. You may have more leaky ones giving you trouble.
R82 and R86 will run rather warm. These are the 510 ohm 1/2 carbons. See if you get the 5.7V on the load side (pins 8 and 9 of U74). These may be high. If your are bad, I suggest using 1W. These are used on S/N 70000 and higher. They are located on the main trigger board between U74 and U122.
I hope this has been of some help. If Dan or anyone else has suggestions, help him out.