Uh oh, not what I expected. The board looks to take mains voltage and rectify it. Then feed some form of timer design. My initial take was there was a center light that was on for X time. When it went off the outer lights came on for X time. They alternated so neither the center or outer lights were ever on at the same time. Now, looking at the picture, I am not sure how they did it. I don't see what looks like any relay in the image, The 4 diodes I think rectify line voltage seem pretty apparent. I am just not sure what you have there. The board does not look to be complex I am just not sure how things are configured to have it do what it does.
Ron