I don't know exactly which mechanism is used in your specific operating car, but Railking generally uses a lever micro-switch as shown in this video (albeit an operating reefer but same idea):
When you initially activate the car (instructions will say press controller for a couple seconds), the mechanism moves such that the lever switch opens. This then applies power to the animation motor and keeps the cycle running after you release the controller. Then when the mechanism completes its cycle (signalman comes back), the lever is tripped which then stops the animation.
The desired scenario is you just have to bend or adjust the arm/lever on the micro-switch.
But...I seem to recall there have been instances of failed lever switches. That is, you manually press the lever arm on the micro-switch, even hear the mechanical "click" of the switch closing, and yet the animation motor continues running. In this case, you need to replace the switch which will involve de-soldering/soldering wires. If that's your scenario at least these switches are inexpensive and widely available (a couple bucks).