In typical Rat Shack style, they don't really tell you what you need to know BUT, no LED I have ever seen drops 12 volts in forward bias (Vf). So this unit has a dropping resistor in the package which looks like you can see it through the case.
Don't let these guys rip you a new one! That red LED and resistor is poor quality at best
50mcd at 45 degrees. Their cost is probably all of 2 cents. Get an LED from some broken item and connect up a scavenged resistor. The color of the LED makes all the difference to the Vf and that's the number needed to calculate the value you need. For just a quick test, pop on a 470 Ohm resistor and hook up to your 12 volts. WATCH the polarity, it is a DIODE after all!
470 Ohms is yellow violet brown
Pay attention to this very complicated answer: NO! No resister is needed. Ready made lamps like this already have the resistor included inside and are rated for the required voltage, in this case 12VDC. There are versions of these lamps that have a diode and resistor for 120VAC, directly, no external components. Bob
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Checking out the URL you provided, I found this component to have a build in
680Ohm resistor already. So you can connect it parallel to the 12V fan. Be sure to connect it in the right direction. You may blow it it you connect it in reverse.
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Most LEDs can handle a maximum reverse voltage of 5V. So unless some precautions are taken, the LED wil get 12V reverse voltage which it cannot stand. Precautions may be a antiparallel diode or even a second LED antiparallel to the first. As I did not see this or any other provision mentioned in the specifications I advise to stay on the safe side.
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