Another thought: what if the two relays on the headlight shell, presumably one for high and one for low beam, are different, and the low beam one has the load (low beam) connected a "normally closed" instead of a "normally open"?
That would do it, I think.
However, looking closely at the photos, it seems likely that they are both the same type. Which leads me to a further thought:
In this photo, we can see two green wires coming from the battery, one from plus, and one from minus
and in this one, assuming the two relays are the same type and mounted the same way around (it looks like they are), on both of them a green wire on the same terminal of each. So what's going on there?
Going by the diagram that @Weegie posted further up, that might be 85 or 86, in which case it might not be relevant (works both ways, assuming there is no diode in there), but it seems odd to me. Or at least sloppy.