I couldn't find the plug for that in any search. Why not replace it with a regular accessory socket? On my old Honda Fourtrax 300 FW I wired in accessory sockets on both the front and on the rear for running accessories .. My Honda has Honda's version of an accessory socket wired in on the front , but like your Yamaha , it is not a normal accessory outlet and although the plug is available the price of it is ridiculous. It uses the same plug as Honda generators use for their 12v DC outlet for battery charging. Most likely the plug you want is no longer used by Yamaha and they've gone to normal accessory sockets when fitted to newer machines. I'd clip those wires at the socket and replace the socket with a regular one that is readily available from any RV outlet. You could leave that unit as is if you wish and plumb in new wires and sockets like I did for power both front and back

I think #1 is the plug https://www.partzilla.com/catalog/yamaha/atv/1999/kodiak-4wd-yfm400fwbl/electrical-2 #59V-81942-00-00 COVER https://www.motosport.com/oem-parts/YAMAHA/1997/bigbear-350-2x4/electrical-alternate I'm just not sure of the hook up there.