Taking a quick look at one of my assemblies...the purple wire goes to the tip connection (positive) of the jack and the black goes to the sleeve (ground) of the jack.
My jack is the kind that disconnects the battery when unplugged, I'm guessing that the red striped and black wire extending out of the photo are for the battery and there is another mechanism to turn off the battery current.
I bet someone who is well versed in this will chime in.
hope this helps a little,