On your probing of pin 18, the ramp will take as long as the sweep, approx. 10x the sweep setting to cover all 10 divisions. If you're measuring with a voltmeter with the prescribed test settings, you'll never see the ramp because it's too fast. One thing you could do is turn the sweep down to 0.5s/div. The sweep across the screen will take about 5 seconds, and you should be able to see such a slowly changing ramp on a voltmeter.
Since you're getting a vertical deflection, you could also probe pin 18 with Ch 1, again at a slow sweep. With this problem on your scope, what you should see is a dot slowly going up and then resetting, repeatedly.
What are you seeing on the back panel A GATE OUT? A logic high here indicates that the A sweep has been triggered.
Does XY mode work? Seems that it probably should given the other symptoms.
I would also try removing and gently cleaning the contacts with isopropyl on hybrids U500 (trigger) and U650 (display sequencer). Don't mess with the nut on U800; it is prone to failure from mechanical stress.