Since my need was for only one side of the ErgoDox, I ended up placing the EEPROM in a different location.
I used some spare USB cable to connect the EEPROM. I had enough and it's colored so I could tell the difference between leads easily.
I used the datasheet from Amtel to identify which leads were which on my package of the chip.
Identifying which contacts for the power was fairly easy since they're labeled on the board (on the other side).

The SCL, and SDA were a little more difficult, but is simply a mirror of the example picture in the first post.

The package of the chip that I got was not ideal. I'm not sure which would be the best, but this one is designed for surface mount and the leads are incredibly small and was a huge pain to solder the wires in place.
The chip lives on the front of the board near the controller in an available space. Luckily there was a hole in the board already through which I could route the wires.
The finished product:

Thanks again to everyone that helped. The firmware has been working quite well.