Notably, you don't need a relay for the RESET pin. Since the Pi and the mobo already share a ground courtesy of the PS/2 connection, you can just tie the RESET

Notably, you don't need a relay for the RESET pin. Since the Pi and the mobo already share a ground courtesy of the PS/2 connection, you can just tie the RESET line to a GPIO pin and leave it floating (configured as an input, high-impedance state) when you don't need to reset the motherboard. When you do, configure it as an output and set it low, which pulls the signal to ground and places the mobo into reset. A moment later, turn it back to an input and the mobo's pullup raises the line and the chips come out of reset. If you're feeling extra cautious, use a small FET and raise the gate to pull the pin low. More details in my other comment here.