It is nothing to do with 12N/12S wiring or 13-pin, it is to do with the vehicle.
Most cars made within the last two or three years use something called Can-Bus (or similar) technology. Basically this means lots of little electronic boxes around the place which get instructions from a computer signalling highway, and then switch the power from a single heavy duty power cable.
As this requires quite a bit of system intelligence it is thence easy to look at the load on the light circuits that feed the the socket and see if it has increased by connection of a trailer. If several circuits are showing increased load - say sidelights, brakelights, and one side flasher, and the other side flasher is not then there is a fair bet that a bulb has failed. This can then easily be brought to the driver's attention.
A simple test to prove this - as in my Astra 5 - is to connect up, set the flasher going, and then unplug the trailer connection. Either the sounder (if there is one) will stop, a light will come on on the dash, or the flashing will significantly increase in speed.