This connector is the programming/diagnostic connector for the speed controller. Do not use it for a power source. It does have 12 volts between the violet and black wires but its only 100mA supply from the speed controller which is being supplied by the high voltage side.
Your best option for adding as accessory such as this is with the center console wiring. 2 speed fan wiring is already present. In the center console you will find a black connector not plugged into anything. It will have red, yellow and blue wires going to it. The blue is the 12V+ with is on the F15 fuse. The red and yellow wires run out of console and go to a 3-pin connector just behind the console. These 3 pin would have black, red and yellow wires going to it.
Wiring for the 2speed fan is shown in this diagram. Towards the lower right.
That would be the correct connector you would be looking for. In our case of the 2-speed fan option this would plug into the fan motor connector. Same as you would see on the blower fan of the DC heater mounted in the center console if equipped.