I'm in the process of wiring up my 12S socket myself. Just going about finding my own way of retro fitting it. I it's wired in properly there's no need to run the wires from the alternator, just use the ones already there.
But more to the point, how you fitting your towbar? Yourself or a garage? Not sure on what is checked on the MOT now, but I'm lead to beloved that the towbar mounts are part of it.