I unplugged it from the white socket to repair the wire - I suspect it may have something to do with the air-con, but that's not worked for many a year and is always set on ECO.
It's now repaired and doesn't make any difference from before. Maybe it took a fuse out when chaffing against the chassis?
It's the A/C compressor clutch connector. When energized an electro magnet near the front of the compressor 'clunks' and locks the compressor drive to the spinney pully that runs off the 'fan' belt. The gubbins in the compressor then start compressing the gas in the A/C system. You can tell if the compressor is engaged because there is triangular shaped assembly on the front of the compressor. If it's stationary with the engine running, then the compressor isn't engaged. If it's spinning, then it is.
However, if there is no gas, or too much gas in the system, then the electronic thought police grass that up to the electrickery, and the compressor is clutch is not powered. There are also fuses and relays which if faulty will stop the compressor clutch engaging.