Hi Pat, sorry to hear you are having problems, to the best of my knowledge any JC ecu inc. gsu before V6 should not operate without a signal from the rx.
V6 is a modern exception to that rule but only because it is designed to stay on after rx power off for auto cooldown then shuts itself down automatically.
So logic dictates the ecu should not be able to operate with the rx turned off even with the ecu power available which to my mind indicates an ecu fault, just my thoughts.
Regards,
Gary.