OK, I will take some scope shots tonight. I'll set the RPM to 200 to simulate cranking on the bench tester. For an in-car measurement it actually doesn't matter whether your scope is battery-powered or powered through mains or a charger.
When I work on my bench-tester I have to ensure I don't short out anything with the oscilloscope GND clip. That's why I prefer my battery-powered portable scope for that.
Below is my bad ignition switch in the ML430. Note there the 4 millisecond pulse with a voltage drop of 8 volts. At the end of the dwell time you can see ringing meaning there is a spark event of sorts. But it is so weak it won't run the engine. The measurement is taken between terminal 30 (perm. +12V battery) and terminal 15 (switched +12V from ignition switch, ON and START) during cranking.