I've been looking the service manual.
I'm not a proficient electronic expert. But It is quite unreasonable for the leds to be on while de reels have stopped.
I'm assuming that when you press "stop" while playing, forwarding or rew, then the tape stops but the lights still light. I'm not facing the "autostop" situation (stop because teh tape ends)
If so, the only cause may be a faulty transistor that drives current from the motor driver circuit back to the led line. The deck has an integrated circuit whose single outputs light the led and control the motor and solenoids. There aren't two wires coming out of this circuit that both mean "play".
When voltage is raised in the play, ff, or rew line, several transsitors make the current flow through the solenoids and the motor.
If the tape reaches the end, you may see it stops running but the logic circuit may not be aware of it, and so it still tries to light the leds and run the motor. That would be a autostops failure, stil strange.