I am not familiar with the Vespa magneto, but I suspect that it works very much like most "energy transfer" systems (I got that name from my old, generic how to fix your motorcycle book).
This is easier to describe with pictures so imagine my hands and arms waving as you read this.
Inside the magneto are one or more coils which provide power to the primary side of the coil only, they have nothing to do with battery charging or lighting. Voltage is induced in this coil by the rotating magnets in the flywheel. This produces a pulsating voltage in phase with the passing of the magnets. One end of the coil is tied to ground and the other end is tied to the moving side of the points. From here, there is a wire to the primary side of the ignition coil, the condensor and somewhere along the way, to the kill switch. As the flywheel rotates and the current in the magneto coil is near maximum, the points open. This creates an instantaneous voltage change from 0 volts (the points had the coil grounded), to maximum voltage. This voltage change is seen by the primary of the ignition coil and induces a high voltage in the coil secondary which causes the spark. Note that this is opposite to a battery/coil ignition where the points being closed cause current flow through the coil and when they open, the collapsing field in the coil causes the spark.
If you check for all of these components and connections, and make sure the insulating washers are installed correctly where the connections are made to the points (the moving contact should only be grounded when the points are closed), you should get a spark.
For reference, the Magneto coil and the Ignition coil primary should each read about 1 ohm or less to ground, the plug wire, without the resistor cap, if you have one, should read 5 to 10 K ohms and the condensor should read infinity except for a slight kick when you first connect the meter.