Hmm… I don't know if "LED Light" quite fits into the ATM argument. In "Light Emitting Diode," "Light Emitting" describes the kind of diode it is, namely one that emits light. There being many kinds of diodes, without the first "Light," we couldn't know what kind of diode this was, thus the purpose of the first "Light."
There being many different kinds of lights, without placing LED in front of another "Light," we wouldn't know what kind of light it was, much like tacking "incandescent" on the front of "light" tells us that the light isn't, say, a fluorescent light or a LED light. Furthermore, with "Light" on the end, we also know more definitively whether it's a LED to be used for a stereo power indicator or for outdoor illumination.
The redundancy of "ATM machine" is that we already know it's a machine. The redundancy of "PIN number" is that we already know it's a number. But with "LED light," the "Light" in LED isn't speaking to the purpose of the LED, but rather to what kind of diode it is, and the second "Light" speaks to the purpose of the LED. Does that make any sense? I'm rereading this, and it seems to, but then, I live in my own private world most of the time, so this could just be gibberish.
In any case, great news! LEDs require a fraction of the power conventional lights do, which means I can light my home for a whole lot less.