Some time ago, I am sure I posted about bad design/difficulty of fitting lights to read of child trailers - in my case the one from the EBC.
Recently discovered a solution. We'd picked up a set of USB rechargable lights in the last EBC sale, and while the rear light does not fit well on any of our seat posts, it fits perfectly around the frame of the trailer. If you were really concerned, you could put one on each corner, and it would be quite spectacularly well-light.