Looking at the JW Speaker web site, it describes the two-pole connector with the red and orange wires as "an extended harness that you will tuck down and plug into the Jeep’s factory turn signal plug".
On the Jeep JK those turn signal lamps also function as a parking lamp, so I assume that is what the "RED WIRE for position" does. Looks like there is an unused 3rd connector position on that plug which is presumably the ground for the Jeep turn signals, which have a 3 wire connector.
You should not need to connect the 'M3W OEM turn signal white ground wire' to anything, although it should be reasonable to also connect it to the 'BLACK WIRE for ground' as a backup ground path.
I would try connecting 12V positive to the red wire just to see if this helps, although that seems unlikely based on the JW Speaker instructions. If it does you'll need to use a source of ignition-on 12V as a permanent solution.
I'm interested to hear if you get this solved as I'm planning a LED upgrade of my M3W when I get the time...
