Sometimes the battery indicator light comes on. My car does not idle smoothly either.
The charging indicator light comes on when your vehicle is not charging or you have an ignition cylinder binding and not coming to the full run position. The ignition switch and key lock cylinder may be at fault. The rough running can be related or may be anything from an engine miss fire to a dirty throttle body and injection system. I recommend you have a mechanic, like ones from YourMechanic, come by and inspect your car for the rough idling issue and then follow up on the indicator light problem.
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