Tripplec, your wiring looks to be what has been stated as correct for the hatch lamp to illuminate the brake light on '07-'09. Mash the pedal to see brakes on the body lamp and hatch lamp. It does NOT do this on the 10-12 years. This post is trying to figure out how to make it work. At one time it was a simple swap, put the '09 wires on the 10. But they have changed the "harness" and now it doesn't work.
Unable to "see" the bumper reflector, it sure looks like there is room there to make a hole and snap in a connector/bulb. Replacement reflectors with LED run about $69. Not too bad.
Looking at my '10 hatch connector, there seems to be a vacant "slot" where the 2nd brass contact should be. But it is molded in, I see no way to insert another brass contact, nor have a wire connected to it. No luck yet finding a dual contact/3 wire connector that fits the Hyundai hole. This is quite a challenge to figure out.