We were in the same boat when we purchased the L322. The queried the dealer and he had a Jeep tongue out the back which is the same and threw that in as well. We don't often use it for towing but during the fires we loaded the car up with our worldy possessions that we didn't want to lose and hooked up the camper trailer and parked it down at the fire station for a weeks. We have a black and white round plug as well. We towed it down during the day and after the threat had passed a few weeks later we bought it back home one night after training. However with he headlights on it would apply the trailer brakes. my wife ended up driving almost a kilometre with this being the end result.
Attachment 158810
almost burnt it to the ground which ironically was the kind of thing we were trying to avoid. I haven't bothered rewiring as it works fine with the other trailer with no brakes and we don't use the L322 as the tow vehicle for the camper.

