To be suddenly struck with an ingenious or inspired idea, insight, or revelation. In this expression, the phrasal verb "go off" means "turn on" or "become active." After nearly four hours trying to come up with a solution, I finally had a light bulb go off in my head about what we needed to do. Hey, I just had a light bulb go off—what if we try rerouting the funds through your sister's company to avoid higher tax rates?