How does this work?

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How does this work?

I mystery electrical engineer showed up taking pity on my trucks idiotic lighting system; installed the if these very nice leds and this teeny little power supply that had a dimmer but broke off. The dimmer breaking just broke the dimming function but the lights still lit at one brightness. When I accidentally tore one of the 3 leds away though, wiring back in only the remaining two, the system quit after a few hours. It's very efficient. How do I reimplement this?

Added
2016-05-27
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