90% of CDi igntions are basically electronic magnetos IE they are powerd directly from the generator and have no connection to the 12 volt system. There are a few out there that use inverters to ramp up the voltage, the very early Kawasaki H1 springs to mind - you can hear the inverter humming when you switch the ignition on. The one in my diagram is a classic example of an AC CDi fitted to hundreds of bikes and uses windings in the generator to provide the high voltage to charge the capacitor.
These systems have one feed wire from the box to the coil, if there is another one its earth. Both are dead with the ignition on bike not running. Don't try and measure these with the engine running - there is a series of 200 volt pulses firing the coil not a steady DC!
Transistor ignitions feed 12 volts to one side of the coil, the other goes to the TCi box. So both sides of the coil will appear live with the ignition on