PS2 Runaway Slave A unit

If slave is disconnected from the master, the slave should not move.  If it does, there's a "stuck-on" component on the slave board.  Inspect the larger black components in the area circled to see if there's anything obvious like a cracked body, dis-colored board under a component, charred remains, whatever...though there may be no visual indications at all.

Photo copied from: https://ogrforum.com/t...or-mth-proto-diesels

With the motors disconnected, does the relay on the slave board "click" when you change directions?  Presumably there is no shorting in either direction with motors disconnected?

You say the front motor by itself shorts but the rear motor by itself does not.  Since the motors are connected in parallel, this suggests the front motor has an internal short or a short in its wiring/harness.  You should be able to find a wiring short by inspection.  To test for a short in the motor itself, if you have a meter measure the resistance between the disconnected motor's terminals and between each terminal and the frame/chassis.  Rotate the motor over 1 revolution and measure at several angles.

Great answer Stan, thank you.  I will try out your suggestions tomorrow.