a light bulb goes on in (one's) head

One is suddenly struck with an ingenious or inspired idea, insight, or revelation. We spent hours trying to come up with a solution, when suddenly a light bulb went on in my head. I kept feeding him subtle hints about the truth of the matter, waiting for a light bulb to go on in his head. Hey, a light bulb just went on in my head—what if we try rerouting the funds through your sister's company to avoid higher tax rates?