Good News: Did some digging behind the steering wheel and found the Fog relay. It seems to be the same size relay as in the Tacoma tutorial. Maybe even the same part number.
Bad News: It's not as simple to wire as it is on the Tacoma. It seems the low beam dependency is before the signal gets to the relay. Maybe the wiring needs to be done underneath the stalk on the steering wheel column.
Good News: I was able to wire the fog light independently by removing the relay and wiring a power source directly to the connection. Now my fogs are on all the time when the key is in the ignition. I will be looking for a separate fog light switch if its a reasonable price but for now I've wired it directly.
Here's a view of entire panel, the fog light relay goes on the bottom left. (it's taken out in the picture)
Closeup of the relay and spot in the panel where it goes.
The Relay.
The top two vertical plugs process the signal that comes from light stalk. If I wire the one from the tacoma tutorial to a power source, the fog light doesn't come on. If I wire the other one to the power source, the fog light works independently when the low beams are off but the fogs go off when the low beams are on.
The top horizontal plug provides power and the bottom one goes to ground. If you put a loop wire in them both it completes the fog circuit and they turn on, even with no keys in the car. So I wired the bottom connection to another power source that is only on when the ignition is on.
Fogs on with no low beams. They even stay on when the high beams are activated.
Now I just need to figure out how to disable the DRLs.