LED Fog Lights on Gen III Prius Four

It seems that Auer Automotive used to offer an LED Fog Light upgrade kit (TPR-813), but it is no longer available, so I bought a kit from an eBay seller for my 2015 Prius Four. It was shipped from a Toyota dealership in California and even came in a Toyota/Lexus carton, but I suspect that it is only the lower grille cover that is actually a genuine part: the fog lights were in unmarked cartons, and the wiring harness came in a padded USPS bag. No installation instructions were included (which I knew from the listing details to expect).

Auer still has an installation video on YouTube, plus installation instructions as a .pdf. These are fine as far as the mechanical/physical installation is concerned, but their wiring harness is a little different from mine. No "tap" connectors are included with this kit, and there is only one relay instead of two. There is a preinstalled connector for the switch; it'll be fun trying to get that through the firewall. A bare-end white wire is connected to the in-line fuse holder that presumably connects to a spare 12V terminal in the fuse box, and there is a skinny bare-end red wire that has continuity with two of the switch contacts; where would I connect this?

Has anyone installed a kit like this?

 

Yes, I saw that one: it's the one I referred to in my original question. But his setup uses two relays -- one by the fuse box and one on the inside; I don't see an overall schematic to figure out why there are two relays. And he brings only two wires through the firewall, whereas the kit I bought has four wires bundled together (two red, one black, one blue) and permanently attached to the switch connector. Maybe I'll just cut those four wires and use bullet connectors to reconnect them -- they're far longer than necessary anyway. Correction: the red wires don't have to go through the firewall from the switch -- they will connect to a 12V-with-Low-beams-only source at at Connector 2C.

 

I connected the "actuator" leads of the relay (actually seems to be a solid-state device -- unless it's simply too quiet for my old ears to hear) between ground and the brown wire in the ECU connector. According to many different posts on the 'Net, this should have 12V only when the parking lights or low beams are on, but my fog lights remain on when I switch to high beams. Is the brown wire the wrong one, or is it because the low beams remain on with the high beams? Is there an alternative connection point that is not powered when the high beams are on? Is this perhaps why the Auer Automotive kit uses two relays?