Depending on how your tail light was broken, your insurance might cover it. For example, comprehensive coverage will cover your broken tail light if it was damaged by a falling tree branch. Collision insurance typically covers a broken tail light if it was damaged in an accident. The other driver's liability insurance might cover your broken tail light if it was damaged in an accident and you were not at fault. But a burned-out light bulb or a defective tail light likely won't be covered by insurance.