I was starting to think ignition switch, you seem to be thinking that also.
I don't have a 1200 sport schematic but I believe it's similar to the Norge, the switch on it shows 6 wires all of which should be alive in the Key On position, if you can find the connector make yourself a Voltage probe with a sewing needle and poke it through the insulation of each wire to make sure it's alive. Perhaps do this on the switch side of the connector (will get replaced if the switch proves to be bad)
The tiny hole the needle makes won't let the magic smoke leak out unless you touch the needle to chassis of course.
A couple of other things
The number plate light and tail light come on with the key, I think they share the yellow wire with the headlight.
All the fuses should be alive with Key On Check for power at both ends, there is often a little opening in the back of the fuse where you can see exposed metal, your needle probe will work there too.