Only one fog light connector on 2003 X

One connection, both sides.

I believe this is blank harness plug for an optional temperature sensor for the auto-dimming rear view mirror. My 04 X also has this plug behind the driver's side front grill, and a blank harness along the bottom of the windshield under the defrost vent trim piece. I bet the mirror and the temp sensor plug right in and work.

Correct. The 03-04 fog light was actually an add on factory accessory on the X. My 04 has it, and it was an after sale install. I have the invoice somewhere, and the little instruction book. It essentially added an extra harness and set of relays on the passenger side firewall the wrapped up along the front passenger fender to the grill area. I also believe it changed the light stalk to include the fog setting, but not sure on that.
Anyways, if you're adding fogs, just go ahead and do an external relay. If your stalk has the Fog setting, a custom kit will likely just add on where the factory does anyhow.