The illuminated bridge is compatible with reference cards. Yours are not reference cards. This is probably the reason why it does'nt work : no circuitry for LED control. (AFAIK, the LEDs are under graphics card control, and the bridge needs the LED controller : the bridge is a passive component). In other words, if the graphics card is already illuminated (like ref cards), it works. If not, it does'nt.
This certainly is a Asus 770 issue, not a NVIDIA or EVGA bridge issue.