I would further test the trigger portion, to see if it ever works.
So no sweep ever if switch on TRIG (compared to AUTO)?
AC and DC coupling, on source Ch1 and Ch2, also external trigger, on the slowest sweep speed, I would test. Does it have LINE trigger?
Most analog scopes will trigger once if you quickly move the TRIG LEVEL pot back and forth, to force a trigger, post trigger pick-off circuit.
Guessing it's usually an oxidized switch, or the trigger input section got overloaded and killed a transistor.
If you can't find a schematic or service manual, I'd follow or (need another scope) the signals at the trig aux input and switches, to at least take you to that PCB section.