When you say "make a small but worthwhile amount of money" from music, what do you mean, exactly? (dollar/pound figure?)
What diverse skills do you have that could be marketed, and what is your market like as far as those skills? (Jobs available, or far too many players looking to scratch a few cents out of the two gigs there?)... Can you play instruments, sing, DJ, and/or otherwise perform in front of a live crowd? Do you have the equipment necessary to do so? Can you teach lessons on an instrument or voice? Do you have a studio that could accommodate outside clientele? What is the advertising market like in your area?
It is certainly possible to do what you describe. I have been "doing music" professionally for over 35 years. But that is with a very diverse set of income streams, some nearly non-existent at times (I have a steady teaching job, and have been a private teacher, live musician, studio musician, live sound engineer, jingle producer, have done all kinds of work in live theater, lighting, DJing, studio owner/proprietor, have done a fair amount of music journalism, etc., etc., etc.). And there is still often a lot more "month left after the money is gone." I know another guy who has done exactly what you described-- he works one job most of the year, and then spends several months working as a solo act in Key West, Florida. There is always a way, but it depends on your abilities, stick-to-itiveness, the amount of money and time you are willing to spend to launch this aspect or these aspects of your career, and a lot on your local/regional market.
Times have always been tough for musicians and artists. They are tougher still nowadays. If you are just looking for supplementary income, part-time jobs are available that would probably cause you a lot less stress. But if you feel like you couldn't possibly do anything else, well...