Even if a material reflects 100% of the incoming light, the light has to bounce around quite often in order to stick around for the time where the LEDs are off. In fact it has to travel 156 km somehow. Suppose a ray hits an object and doesn't get reflected. Then it has to be reflected at the right angle to hit another object, and another one and another one, until it has traveled the 156 km. Each time, it can also be reflected into the sky or be absorbed. I'd argue that within the time, most of the light will have escaped or been absorbed. Unless there are materials that have an after glow like you describe.