When the word plumber was first borrowed in the late 1300s, there were still over two centuries until the flush toilet was to be invented. At the time, the occupation was very different from today's stereotype, and the job description included working with any kind of lead. Later on, as running water began getting implemented everywhere, the pipes being used were chiefly made out of lead, so plumbers became associated with toilets and piping. The rest is history, but let's zoom backwards in time now. Plumber developed from Old French plomier, which meant "lead-smelter", and that's straight from Latin plumbarius, "worker in lead". The root is plumbum, which meant "lead" and is the reason why the chemical symbol for lead is Pb. Beyond that, things get hazy. There is a cognate in Greek, but it doesn't seem Indo-European. Maybe Etruscan or Iberian? Who knows. Point is, it's an interesting etymology.
Adam Aleksic, a rising sophomore studying linguistics and government at Harvard University, has been described as the internet's sixth most famous etymologist. He also has disturbing interests in politics, vexillology, geography, board games, conlanging, and law.