You must find out why your battery light isn't illuminating. Have you pulled all the fuses and checked them all? If the battery light does not come on, the alternator will not charge the battery. Pull the cluster and check the filaments of the bulbs. Clean all the ground contacts too.

Its a little confusing, because you say when the car is idling the volts on the battery is 12.7v....that means its charging, but if the battery light does not illuminate....how's that possible?

Has someone been messing with your electrical system? What about these led lights? Is the stereo aftermarket? With subs and an amp?

I am wondering if your just over running your charging system. These cars aren't generators.....typically if you plan to use all your house hold gadgets and every accessories in the car....you really need to upgrade the charging system, thicker wires...beefer alternator....dual pulley alternator....maybe even a solar panel...

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