BC could mean "bridge circuit" by the looks of it, but I can't find anything that lists that abbreviation in a circuit diagram. That trace appears to lead to the keyboard controller. My guess is that "BC12" uses the same capacitor as "BC13", and part of the Resistor network (RN)?

[EDIT]

Also, D3 and D4 are supposed to be diodes, but it looks like just straight jumpers, which doesn't seem right.

I have had no issues whatsoever with keyboard not found or anything of that nature. I did re flow some solder joints on the AT power supply pins and so far the system has posted about 20 times in a row. Not sure if BC12 is needed, but I can tell from the pads that something looks to have been there at one time.

Got the multimeter out and I do get 5 volts on the Right pad of BC12, nothing on the left side. Continuity tests on the left show that the other side of the pad goes to about 3 different pins on the Amikey chip.

Check continuity vs 5V and GND on the power connector. if they are zero ohms it's a small capacitor.

The pad on the left of BC12 does go directly to ground as the meter beeps when I put the other probe to the AT connector ground pin 6. I tested the other two BC parts in that area and the meter shows 4.71mF. I know nothing about capacitors this small, does that sound like an exceptable value to connect to BC12? I did a few google searches and I can find a picture of this board, and there is indeed something in the BC12 spot, however it seems to work fine other than the occasional POST glitch.

You can't measure the caps that are still on the motherboard, you are measuring all caps summed together, and every chip that loads the supplies will affect the measurement as well.