Please post images here instead of using dropbox.
It is almost certainly a small microcontroller. They cost almost nothing and with a few lines of code can be made to do all kinds of things. The middle 'zigzag' is two contacts which would be joined by a carbon pad when the switch is pushed, that sends a signal to the micro which sets the place in a sequence of the three conditions you describe. I have something similar that also has two brightness levels, achieved by flashing the LED so fast that the eye perceives it as a steady lower brightness.
Brian.