I was just looking at this. The EPC shows another switch 003 545 90 24 that "as of" engine 7230 that is considerably cheaper ($177 list).
If that's a budget-buster, you can try the time-honored work-around of connecting the pink wire to ground. That way the cold-start valve will fire the whole time the starter is cranking, or you can wire in a push-button switch between the pink wire and ground to control the valve.
But I've got to ask, are you sure it's the TTS and not the relay?