I have an old telequipment I use now & again.
Yes you can put the sqaure wave on one of the channels and the trigger i/p at the same time.
I had a problem with mine regarding the trigger, the vertical attenuator switch was grounded to the chassis via the threads & nut, but it had corroded creating an open, taking it all apart was a right pain, so I soldered a wire from the switch to the chassis, trigger now works perfect, the other thing that was messed up was the vertical position control for one channel, it was so sensitive you couldnt get the trace to stay on screen.