Well, I'm confused now :?
Just had a quick look between the rain showers. The relay is only a single pole relay, so one switched path to power both left and right sides. However, testing for continuity for the main beam (white wire) between the left and right bulb holders gives an open circuit unless the headlights are selected to main beam. Then, you get continuity between left/right and +12V at both sides when measured to ground. Either they are wired up in a weird and wonderful way or, theres something else between the relay and the headlight which is controling the main beam.
You could try swapping the relays over for dip/main beams in the top of the glove box, but they are slightly difficult to get to... and I doubt that would cure it or swap the fault to dip beam