Only charge capacitor when button pushed then turn on 12 VDC motor momentarily with capacitor when button released
You can use an optocoupler if the motor is small, otherwise, you can use the output of the optocoupler to turn on the motor driver. Here is the circuit of the optocoupler, notice the LED that turns on the transistor on the other side.



Here is the circuit with the optocoupler substituting the LED:






simulate this circuit &ndash; Schematic created using CircuitLab