I did it myself as my first change to my Santa Fe. It was very easy. No issues and don't expect any. You need a piece of wire and a splicer and a pair if pliers. The splicer is usually blue and can be found at mist electronics and auto parts stores.
I just performed this Fog light Mod on my 2011 Santa Fe SE. using the scotchlok connector I tapped on the brown/orange wire to ground. i did not have to cut the wire..the fog lights work when the key is on and work independently using any combination of the parking or headlights.
I believe all the details are here. Its been a year since I did it. One of my pic's as well is in the thread with the cut. Can be done in the winter on a sunny day unless you have a garage it don't matter Not hard just pay attention to what you have to do.
Thanks for the thread link, especially the video. It's much simpler than I thought: Cut the brn/orn wire from the switch and ground it so the ground won't be dependent on a circuit through another controlling relay. Since I have background in such things (several avionics specialties in the Air Force and Air National Guard, as well as way over twenty years as a building controls specialist), it makes perfect sense. Now I have to make an educated guess about whether this mod will do any damage to the used car warranty I got when I bought the car last month. Details, details.
About bulbs: I replaced the stock 881's with SilverStar 880ST's. The connector retainers are different but the pins and shells will mate. Us geezers like things lit up.