Before fault can be apportioned to any component, I'd first quickly check the following in sequence:
1- Earth strap to engine not loose - engines can run with no earth strap due to the choke cable etc, still providing ground for small current loads.
2- Remove starter lead spade terminal, and fit a jump wire in its place. When this wire is connected to the battery positive, does the starter fire? if not, then the solenoid is probably faulty. Solenoids can become sticky for various reasons (gunged with old oil, grit and sometimes abrasion seizure etc.)
3- If it fires, then check the starter lead gets 12V at the solenoid terminal when turning the ignition switch to 'crank'. If not, then the ignition switch is the fault. If it does get power, but still won't fire, then there may be a voltage drop across corroded ignition switch contacts etc., whereupon fitting a relay as suggested previously should cure the fault without needing to replace the ignition switch.
Generally, Italian electrics are not the finest, and I once had a problem where my race car would misfire horribly and cut out through fast corners. After an exhaustive search for the fault, including multiple carb overhauls, wiring replacement etc., we found that the keys encountering cornering forces would momentarily move the switch contacts to open circuit!