wiring foglights to turn on/off with parking lights

Relay

OK, a relay is a electronic switch that switches on/off another switch that controls another circuit (Fog lights).
It's like using a fire cracker to ignite a stick of dynamite.
The white wire, if powered by your park lights, will, when the park lights are turned on, flick the other switch in the relay and send power to the fog lights.
You are using the park lights in place of the remote switch.
The red and black wires on your remote switch simply turn the power on and off to the white wire that goes to the relay.
You do not need the remote switch and all of the wires connected to it.
Just run a wire from the hot wire on your park lights, to the terminal on the relay that the white wire is suppose to go to.
There are probably three wires on each of your park lights.
1- Turn signal light
2- Park light
3- Ground
The turn signal lights are independent wires to the signal lever.
Both park lights are connected to the same wire so you don't need to run a seperate relay feed white wire to each of your park lights. Just use the most convient tap in location on one of the park lights.

Dual relays

I can not tell you by wire color what wire goes where.
I can tell you what wire to connect to what pin on the relay(s).
You need to unplug the wire plug fron the relay(s) to identify the numbers on each relay pin.
If you can do that, here's how to wire your project;
You will have one relay for each fog light....for some dumb reason.
You either have a 4 pin relay or a 5 pin relay....doesn't matter.
Pins 86 and 87 connect together inside the relay and do the same thing. More on this later.
Pin# 30 on each relay needs to connect to the battery POS.
Pin # 85 needs to connect together and go to chassis ground.
Pin # 86 wires needs to be twisted together and connect to the park light 'pos' wire. Do not cut the park wire, just tap into it.
Pin # 87 or 87A (Both connect together inside the relay) on each relay goes to one fog light. So pin 87 on one relay goes to one fog light, Pin 87 on the other relay goes to the other fog light.
The black wire on the fog lights are ground wires and need to go to chassis ground.
So now, when you turn on the park lights, juice will go to pin # 86 on both relays.
That will flick a switch inside the relay that allows juice from the battery to enter pin # 30 and connect to pin # 87 (And 87A).
Juice will then have a connection from pin #87 on each relay to go to the fog light that particular relay is connected to.
Make sure Pins # 85 are grounded good, and the fog lights are grounded.
Your fuse should be wired into the wire that goes to the battery (Pin # 30)
Let me know.