Motor for Steering Problem

There would have been end stop feedback from a contact plate inside that servo. I have seen quite a few in rc toys. It uses a regular brushed motor but normally there is a little round contactor that rotates against a pcb inside that gives some feedback when the motor hits it's end limits. What are you doing with the green and yellow wires? I would investigate what happens to those wires when it rotates.
You may find it easier to replace the whole thing with a regular servo.