I was thinking of adding the high beam-triggered relay to the existing system, leaving the existing wiring in place.
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With the fog light's OE switch configuration, would there be a problem if the circuit was back-powered?
so I understand your intent correctly: you want to leave OEM wiring exactly as is but splice in a wire harness using the high beam wiring as a trigger ?
this might be possible but kinda risky, not sure what that will do to the electrical system,
you're basically suggesting adding a parallel circuit to the OEM one, you still need to connect the wire harness relay the to battery and splice into the + and - of each fog to the wire harness and splice in the high beam to trigger the relay.
Honestly, I don't see the value in that, you still need to have the low beam headlights on to have the foglights on if you're keeping the OEM circuit,
you're better off de-coupling the foglights completely from your OEM wiring completely and protect your OEM wiring and use the aftermarket wire harness,
The harness is nothing more than a direct connection to your battery to provide power to the fogs with a relay (mechanical switch) in between the lights and battery that is triggered by any power source. if you want to control them even more add a on/off switch in between the trigger and harness and mount the switch to driver cabin.
have the harness trigger wire connect to parking lights and then the foglights can be ON independently of the headlights and still be on with high beams, in other words, the fogs are no longer controlled by the car,
they are controlled by the aftermarket wire harness relay and you choose what you want to trigger it , be it parking lights, low beam lights, high beam lights, or you can add a switch and break the trigger circuit so you can control it whenever you want.
I suggested the parking lights as a safety measure in case you forget to turn off your lights the parking lights will shutoff after a minute when car is turned off, and that will trigger the relay to turn off and protect your battery from draining.
here's a good diagram of an aftermarket wire harness, the trigger is what you choose to turn it lights on or off
http://i140.photobucket.com/albums/r18/crazycow2/Odyssey%20Fog%20How%20To/tn_FoglightWiringLayout.jpg