Re: restrictive conditions?
In Italy having a second job is not illegal - but there are restrictions for employees. First - the confidentiality/competition requirements, second, the total working time. The latter can't exceed 48h per week, and 13h per day with at least 11h of rest. Employers are accountable for exceeding that.
Of course if the second job is self-employed there are not work time limitations - but the confidentiality and competition requirements stands. Anyway, using an employer tools to perform a second job is a no-no.
Then there specific sector restrictions - public sector employee can't have a second job, including military personnel. Recently a non-commissioned officer went into troubles because he was caught working for Uber.
But I wonder why someone should disclose "if they play in a band" - unless they do it as a band employee.
When I occasionally did some work for an old customer of a company that went bust years ago - I disclosed it to my current employee (completely different business, anyway - the customer is a museum. also). But when I sold some photographs of mine taken on my own time was not any business of theirs - although the revenue service could be interested in it as well...