I don't have an oil light, just a pressure gauge. And I don't own a car...just a couple of boats...heh.
So the light goes OFF when the pressure's low? Or are you saying that the light blinks on at "ignition" and then goes off in a couple of seconds? Anyway, I don't have it.
Basically, when I switch the key to ON, only the panel indicator lights light. I then hit the glow plug button and then the starter button. I have no "kill cable", either, which I've seen. I simply turn the key, meaning it's just a solenoid like my propane system. If it were to break, I would stuff a rag in the air intake, I suppose, to kill the engine. Then I guess I could hotwire the starter if I couldn't get it fixed quickly.
I've seen the low pressure sensors on Atomic 4s, but a lot of A4 owners buy a four-buck "squealing pig alarm" from electronics supply stores. That's basically what I want to install on my diesel.