I have no brake lights on my 2006 Mazda5 van. It went thru inspection 3 months ago and I admit that I don't preflight so I'm not sure when it occurred. They work sometimes with the key off or on but ...

If your car's brake lights stay on even when the engine is off, the brake light switch -- a small, innocuous electrical part you'd only see once something goes wrong with it -- is likely the culprit.