Just had another thought. What if you put a solar battery charger in the VX somewhere. The 12v signal from that could be used to trigger the relay. Then when there was not enough sun to provide current from the solar charger, the low beams would work. Only problem with this is the sensitivity of the charger, because your headlights wouldnt work as long as the charger is getting adequate sunlight.

It should be much easier to wire it to do everything you want by using 2 different relays. If you are ok doing that I can come up with a wiring diagram for that.