I'm getting closer...
That relay box is(according to Google) the headlight relay switch. pn#38660-56b00
I tested the relay, and it seems to be okay. The connector at the harness is burnt across 3 wires, red-white, red-blue and red-green, but none of the wires are touching. Now, I have to find out where these wires go, and hopefully find... well, something! Fun Fun!!