I assume it's only a starter issue and the bike runs fine once started
http://www.thisoldtractor.com/guzzi007/schematics/1999_V11_sport.gifLook at this schematic, it shows a Black/white wire from the starter button thru connector 35, thru a bullet connector to the clutch switch, thru another bullet connector to the start relay, Somewhere in between button and relay you are loosing voltage.
Perhaps you have a wire where the conductors have snapped under the insulation, they will do that if they flex at one spot.
With the key off using your multi-meter you should read about 100 Ohms on one side of the clutch switch to chassis (this is the start relay coil). Move the bars back and forth, if it's ok there then move the meter probe to the start button and chassis, with the clutch pulled in it should read ~100 Ohms as well, again move the bars sooner or later you will find the open circuit.
If all else fails just run a new wire.
You can also trace it the other way, with the key on you should see 12 Volts at the clutch switch to chassis when you push the Start button.
Electrical troubleshooting is just a matter of guess-work and elimination.