Well just looked at the mechanism operation description in the service manual, the direction switching solenoid (green wires) is only activated during forward play.
So that could be a mechanical problem or oxidation of the autoreverse switch.
Anyway it's also good to stop for a time and get back after getting more experience, that's what I've done on the first CT-50R.
Edit : If you test the reverse mode without tape the automatic stop will engages as the right spindle is not spinning (rotation sensor is on the tape counter pulley).