You can wire it with a relay. Why did you want to? The reason they don't do it is because people forget to turn on their headlights later on if the driving lights are on. Most people with a QX just set the lights for Auto. That's what I do wth the Mada. Also, people want the parking lights on at all times because it makes you more noticable. I've heard people wanting the driving on with the high beams. Illegal, but I understand that one.
The fog lights have a higher draw on the Armada. You may blow a fuse or worse yet have a fire if you just jump the wires. I had a fire in my camaro from doing this without a fuse or relay.
The correct and safe way is to follow these instructions.
Run a wire from + battery to the relay. (use a fuse by the battery here)
Run a wire from parking lights + to the relay.
Run a ground to the relay.
Run a wire from the fogs + to the relay.
Plug the Battery + to the top wire on the relay. (The spade of the relay is perpendicular to the other ones.)
Plug the + to the driving lights to the bottom spade.
Plug the + from the parking lights to the left or right and the ground to the other spade, left or right.
When you turn on your parking lights, the relay will trigger but put no additional load on the wires so you won't blow a fuse or melt a wire. The relay will then take the + source from the battery to the lights.
Simple and cheap to do. Should take about an hour with crimps, meter, etc. Use crimps, not tape and use a meter to find the correct wires before cutting. If you want to get fancy, you can hook the relay up to a switch between the parking + wire and the relay. This will allow you with a flick of the switch to make it work stock or work with the parking lights.
You can also hook up the fogs to work with the high beams the same way. Just put High beams in the directions where it says parking lights and they will work with the high beams. This is illegal for street use.(disclaimer)