It would not surprise me if you can find the CTS connector locally. VW and Audi dealers will probably have the connector, but possibly not with the pigtail.
I don't have my wiring diagrams handy, but your comments about connecting or not connecting the ECU not making a difference is intriguing. I seem to remember the dual relay being grounded through the ECU, so the fuel pump should not run at all with the ECU disconnected. Is this the case? I.e. with the ECU disconnected and ignition on, does the fuel pump turn on when you open the AFM flap?
You had been following the "engine starts, then stops" section in the trouble shooting guide, but the starting part you see might be a fluke (seeing as the ECU does not make a difference), so perhaps start at the "engine does not start" section instead?
Pulling a fuel injector is a lot of work, the hose going to each injector is short and stiff, so I don't know how feasible it is to pull just one to check. Other in the forum might have experience with this, I don't.
As for the grounding of pin 5 at the ECU connector, I dont know that there is much mystery left here. Perhaps I have misread your posts, but this is my understanding:
- You consistently see continuity between pin 13 of the ECU connector and one side of the CTS connector.
- You don't see continuity to ground at either pin of the CTS connector
- When the ring terminal at the valve cover is screwed down, you see continuity between pin 5 at the ECU and ground.
- When the ground terminal at the valve cover is floating in the air, you do not see continuity between ground and pin 5 at the ECU.
Have I understood this correctly? If so, it would seem that the wire from the ring terminal to the CTS has at least one more break in it (in addition the the one you found at the CTS connector), and that the wire from pin 5 at the ECU connector to the ring terminal is just fine. The ring terminal is used to pick up ground for the CTS and part of the ECU, it is not used to ground the valve cover.
To test the signal to the injector, you might try to hook up an LED with a 470 Ohm series resistor. Connect the resistor to the anode side (longer of the two pins and the one on the side without a flat spot on the lens) of the LED.
One pin of the injector connector has constant battery voltage on it as long as the ignition is on (The ECU must be connected also, again due to the dual relay begin grounded through the ECU). Connect the other end of the resistor to this pin. Connect the cathode end of the LED (the shorter of the two pins, there is a flat spot on the lens by this pin) to the remaining pin of the fuel injector connector.
An LED is much faster to turn on and off than an incandescent bulb, so the LED will allow you to see the pulses better. Does the LED flash when you are cranking the engine? Does it keep flashing after you release the key?