Your N-channel mosfet is connected wrong and is "high-side" as well.
Here is one of very many tutorials that explains those errors:
Using the Power MOSFET as a Switch
In summary:
1) Source should go to ground; Drain should go to positive supply. Usually, Drain goes to load (i.e., the ground side of the load), which I also suggest you do here. That configuration is called, "low-side."
2) In "high-side", Drain goes to +12V (as you show) and Source goes to load. BUT, the gate in that case must be driven by 12V + the gate turn-on voltage. For normal mosfets, that is about 10V. Thus, your gate must be about 22V referenced to ground to work. The reason for that is that the N-channel mosfet turns on when the gate-source voltage (Vgs) is about 10 volts. If the mosfet is doing its job and there is minimal voltage drop across it, the source voltage ≈ drain voltage. Thus, in high-side, the gate must be drain voltage + 10V.
John
Edit: Why did you pick that mosfet, particularly that package?
Edit#2:
Is your Audi an A4? I did a quick search on Audi ignition to try to figure what all the connections you show did. If you have that A4 temperamental ignition, I wouldn't mess with it. Do you have any technical information about the ignition module you are using?
You mention using a signal generator. Can you give more detail about how you are driving the gate? Although it is said that the mosfet gate is voltage controlled, in order to get the gate voltage to change rapidly for rapid switching, you need to charge it with a substantial current. For example, dedicated gate drivers will provide 500 mA to several amps briefly.