OK, so the motor has TWO connections, not six and the 'relay' is actually a switch is presumably driven by the mechanism.
What we don't know is how the switch operates with respect to the mechanism position or what the motor red and black wires are connected to.
I would guess it works like this: without power, the switch NC connects the 12V input to the motor. When power is applied, the motor rotates the mechanism until it reaches its end position, the switch NC then opens and stops the motor. When the 12V is then applied to the NO connection the motor continues back to it 'home' position where the switch again operates to stop it until the next cycle is started.
Can you see where the motor wires go to on the board?
Brian.