Its not as much a plunger as a solenoid controlled shutter, like that of a camera. When you apply 12v to the solenoid, the shutter flips out of the way, to allow the light produced from the bulb, and reflected from the bowl to enter both the top and bottom of the Plano Convex lens. By allowing the light to go through the bottom on the back, the light then comes out of the top of the outer part of the lens, giving you identical output in a different spot.

I highly doubt the Solenoid is damaged, as these are literally indestructible under most circumstances. My guess, is a wiring issue. I'm sure they are listed in the diagram as having a certain polarity, but it really shouldn't matter. I would look for breaks in the harness, or if there is a more of a main harness that attaches to the light, look for bad/bent pins, corrosion and other problems.