I drew a sketch. I hope it helps. Assume pigtail is disconnected from socket, as are the wires to the lamps. My voltage drop is occurring "upriver" of where I expect it. I figured on $12\,\mathrm{V}$ all the way to the lamps, then $0\,\mathrm{V}$ after, with both brown and black having to keep the same reading. Looks like I don't understand this.