That's a bummer!

Have you done the test on it? I'd still test it before buying a new one. Should be in the TSRM for what resistance is on your particular switch. I also think the two wires going into the switch should be reading 12V when you start the vehicle. Might wanna check that too while you're at it.

There's a used one on Ebay right now, ~$75.00, but I'd try Yota Yard first like SanDiego suggested.

Alternatively, you could bypass it completely if you don't mind playing with a pushbutton switch whenever you start the vehicle! Hold switch down to activate the cold start injector, then as soon as it starts idling rough, let go to turn off the cold start injector, but this would be pretty "hooptie"!!! Still, if cost is an issue for now, doing this temporarily would be okay.