A new oil pressure switch arrived this morning. I had already decided to future-proof the system and bought one of these:
It's a 3 way system, so you screw it into the engine where the old sensor went and then you can screw in the new sensor and also you can screw in a separate oil pressure sending unit for when I get a standalone Oil Pressure Gauge.
To stop oil gushing out I have temporarily screwed the old broken sensor in the top hole until I get the sender. Interestingly, all the threads are tapered to make a good fit when lightly tightened. It was designed so you didn't have to use PTFE tape. But the new unit recommended you still use PTFE tape, so I did. Result: Works perfectly, light works as expected and no leak.