its very likely the outlander does have canbus wiring/lighting, not 100% sure about the lighting ecu set up on the mitsubishi but i can tell you that a lot of cars thesedays (vauxhall in particular) have a shut down system on each lighting circuit so in the event of a bulb failure it shuts off the power to that particular circuit until the bulb is replaced, (well actually it shuts it down until the ignition switch is turned off and on again, then if it see's that the bulb is still faulty is shuts it down again)
this has nothing to do with canbus, however if whoever wired in your 13 pin relay box hasn't done a particularly good job or even skipped the relay box altogether and tried to wire the trailer lights directly into the back lights in the car then the canbus will sense an overload on the circuit and shut it down. (this would be evident if the cars lights stop working at the same time as the caravans.)
failing that it may be time to physically check the 13 pin cables and where its been wired in. I've seen some proper shoddy wiring jobs on trailer sockets in my time.