Your right it is RJ11 at the phone end. Just looked up the phone model, they are ancient Inter-Tel 8520 digital phones.
Still can't find the correct cable. 431A wiring is gap, 4 wires, gap. The ones I need are 2 wires, 2 gaps, 2 wires. I've considered trying 631A, but can't find anywhere that sells 5m.