I don't know enough of the FW spec to help you on that exactly, but I did find a bunch of USB controlled GPIO blocks that give you lines you can use to control relays. I'd doubt that FW ping would work as you're saying, cuz the ping signal would be a data stream, so it won't be a consistent voltage. This would mean your relay would be tripping on and off very fast. There may be something like this USB GPIO card available for FW if you really want to use FW.

GPIO Card: