I don't own one unfortunately James, I tried so many fixes on this occasion that I can't pinpoint exactly when I finally got both brake lights working, and being an intermittent fault I probably never will (I'm just glad I don't have to put up with one more person saying "maaaate, your brake light's out, you're gonna get a fine..." when they had been working perfectly only ten minutes before?️).

Re the wire taps/splices I couldn't agree more, you can see in the final photo a couple of black ones that feed the trailer connector, don't know that I can be bothered doing anything about them unless I have another warning light come on...