Not that anyone seems to be paying attention but I wil give an update anyways.
I found that, indeed, the idiot light LED was missing. I swiped it from my old board and soldered it on. Tested it out and....no dice.
Turns out there are also little "control chips" on the board that feed each LED. I found the one that controlled the idiot LED though and swapped it over too. It worked!!! I now have a fully functional LCI light switch with a rear fog button!
1. Location of the idiot LED
2. Location of the idiot LED control chip. Similar to the ones next to it.
3. Locations of the rear fog LED and control chip (wasn't present on this board as it is the OEM one from my car).