--- You should be able to resolve them very easily.
With the X10 probe DC coupled and its input grounded, set the scope
per box, calibrated, the trigger to 'AUTO' to let it free-run, and the trace at mid-scale.
Set the vertical attenuator to about 5V per box, and the trigger source to about 0.5 positive from 'A'.
Assuming that the pulses from the GM tube are positive-going - that is, they come from the cathode of the tube - connect the X10 probe to the output end of the coupling cap from the GM tube.
Turn on the Geiger counter and ascertain that you can see randomly occurring positive-going pulses on the scope. If you can't, increase the vertical sensitivity until you get to 1V per box. If you still can't, - STOP - something's wrong.
If you _can_ see pulses, set the trigger to 'NORMAL' and adjust the trigger level until you can see the high-going edges of pulses starting stably at the left-hand side of the screen.
Now, set the horizontal to "SINGLE SWEEP" and press the "TRIGGER" button to capture a pulse.
I don't have a 2232, so the front panel legends may be different from what I posted, but...