Headlights Opposites

[limax2]

You took your beating well Alexander  :lol . Further thoughts from me. Are you sure the dip beam is staying on when the dip switch is in the high beam position? i.e both elements in each twin filament bulb glowing bright. If not it could be that the second relay, (with five wires going to it), which controls high/low beam is stuck in the high position. That relay is energized for high beam so would normally revert to dip, but it could be stuck. Or it could be that the dip switch is not breaking contact when you switch to dip and control power is still going to the relay. That is through the yellow wire from the dip switch which should be live in high position and dead in dip position. Hope that helps.
I don't have a foxeye set-up but I think those relays are behind the headlamp. I could be wrong on that.