Check the plug connector has not been damaged by water behind the headlight shell?
Check the Left handlebar switch connector under the tank is also not water damaged ? (or a wire broke inside being pulled when you turned right)
Lastly, the lights are controlled by a relay , the relay is 4pins. However , next to the battery SOME (not all) GV125-S have a small black box with loads of fuses , look for the one that says “headlight” and check it (don’t replace with a bigger fuse or you will fry the harness)
Relay = It is needed for every GV125, it’s always there. (It clicks confirming its sending power to the lights) , it will be in a row of other relays controlling the pump, ecu, injectors etc…. It’s not always easy to tell which is which. If in doubt , disconnect one relay ==> if the pump stops ==> put a sticker there saying its a “pump relay” etc.
Also check for water invasions under the relay rack