1988 Audi 90 cold start injector not working

I am currently working on a problem with a 1988 Audi 90, 4 cylinder, not Quattro.

The cold start injector never receives a signal, so cold starting is a problem, but it still starts after much cranking. After testing the injector (works great), I have presently connected the cold start injector directly to the "crank" signal, active every time the ignition is turned to start (crank). This fixed the cold start problem beautifully, but, as expected, results in flooding when trying to start a warm/hot engine as the cold start injector is not needed/wanted when starting hot/warm.

Other than putting in a manual switch for the cold start injector, a last resort solution, what suggestions does anyone have for a proper fix? What sensors are involved in creating a permissive for the cold start injector? Additionally, where are these sensors - I do not have a manual for this vehicle?

Thanks in advance for your collective assistance.