(Feb. 6, 2022)
Three lines coming in from controller over 3-pin JST:
I put a volt meter on the purple line coming out of the control box. It was usually at zero volts relative to GND, but went to ~3V when I turned on the headlamp.
I had a RFP12N10L logic-level N-channel MOSFET on hand that I think will do the job
One weird thing is that the headlamp's power line is blue and its ground is red, so I had to wire up the JST connectors in a way that looks incorrect.