FOG LIGHT ISSUES

You only have the switch or relay left
to blame
Pop the dash bezel off by pulling all the knobs off and there are some Phillips head screws behind the outside knobs
Take the screws out and then you can
Pop the bezel off and you can get to the switch.
You can disconnect the switch and jump the wires with a test light
And you should figure it from there
The relay is in a blind spot and is a pita to
Deal with
There is a very good detailed thread on the relays in the electrical section.
I added fogs and had a repo switch that didn't work and it took me a while to install the relay
But I figured it out with the help found here

My .02
I only just got my 06 this past January. I immediately installed fog lights that I bought off of Amazon, but had lots of good reviews. I had purchased an OEM relay. I had printed out the OEM fog light install instructions, and watched several Youtube videos on how to do it. The hardest part is supposed to be the relay, and I was able to do that with little effort. Everything seemed to fit, and plug in as it should. I tried to get the fogs to work, and they wouldnt work. I reinstalled everything again. I even swapped out the bulbs that came with the fog lights just to make sure that they werent bad. It turned out that the supplied switch was "sort of" bad.

Try the fogs this way. Make sure your headlights are turned on, and powered with the ignition key turned. Have someone stand in front of the car, or make sure you can get a good enough reflection from the front.

SLOWLY move the switch to the "on" position. As you do this, check to see if they come on at all, even momentarily, and also LISTEN to hear for the click in the relay. I was hearing the click, so I knew that the relay was good. Upon hearing the click, I was able to see that my lights were turning on momentarily, and then going off.

I had three switches sent to me from the Amazon dealer. They are all trash. I can get my fogs to stay on, but there is a sweet spot between off, and on, where the lights will stay on. It took three switches to find one, that will "stay" in this position. However, if I push the switch to the fully "on" position, the lights will go off.

If you have an OEM-TYPE switch, and not an actual OEM, they aren't made too well, in my experience, and the switch could be the culprit.

I feel sure by following the guidance of superbee 4406 and WhiteBread you will locate the lack of a complete circuit for the lights.
If not, here is a far-fetched consideration; possibly, but not probably, the lamps are not plugged in at the xB's front.

To my memory, the RS02 did not come standard equipped with foglamps. They were a Scion option, Part Number 08590-52820, including the lamps, relay, and switch.

These could be added by a dealership or by an individual. The wiring harness was already factory included and only the four items needed to be installed. After the knock-out covers were removed at the front, the wiring and plug could be reached at where they were taped out of the way.

While the lamps being left unplugged are not likely, it is possible. At least it is an easy conformation.
Regardless, good luck with the issue.