The aux air valve won't be your issue. If the car runs with some pedal but won't idle, then maybe it's something to think about. But not running at all? Won't be your aux air valve.
Leaky cold start injector, or leaky injectors generally, is the right place to start. It is relatively easy to diagnose, you pull the injectors and put them in bottles. 390ml coke bottles are a good size. Then you lift the air flap with the motor off, system springs to life, and you can check the fan pattern and opening and closing of the injectors. You want to see a nice even fan from very low airflow all the way up to max airflow.
It's also I think possible to reverse the wiring between the aux air valve and the cold start injector, so you should also attach 12V test lamps across the Aux valve plug and the cold start plug. You are wanting to see the aux valve powered at all times. You want to see the cold start valve illuminate for a few seconds at most when you first switch the car on, then go out and stay out.
If you are wanting a very convenient tool for testing the wiring connectors in KJet, I recommend one of these: https://www.australianonlinecarparts.com.au/gm-pfi-bosch-2-noid-light
Ruling out electrical issues and injector issues, you'd next want to get a KJet fuel pressure tester and check your pressures (control, system, rest).
If your system pressure is off, you have a fuel delivery issue. If your control pressure is off, you have a problem with the control pressure regulator a.k.a. warm-up regulator. If your fuel pressure needle doesn't sit still but vibrates constantly, that's a faulty fuel accumulator, the vibration is the pulsing of the fuel pump (it can cause really bad running if the pressures aren't stable).
If your pressures are correct, you maybe have a mixture issue but KJet has a good reputation for holding its calibrated mixture even after 40+ years of use, so that's not super likely. You'd need a CO tester to tune it anyway, it is very sensitive.
Otherwise it would have to be a motor timing or ignition timing or some other ignition issue.