Download the 2465a-and-2467-service-manual linked in post #2.
Go to the block diagram on page 10-4
Locate CH 2 OUT and follow it back to the CH 2 preamp.
Notice how Module 6 is the vertical channel switch.
You will need to somehow take the output from after that channel selection switch to the CH 2 OUT.
Page 10-23b shows the output from the selection switch is a differential voltage, from the switch through the vertical amplifier, U600, to the beam deflection.
You will need to find a difference amplifier, to convert the differential signal to a single-sided signal, that can go to the repurposed CH 2 output.
What bandwidth do you require for your selected output signal ?