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The battery light is controlled by the internal voltage inside the alternator and often times the alternator will continue to charge but replacing or checking for good connection at the voltage regulator. In most case it requires replacing the alternator. Running this test will verify.
Verify there is battery voltage on the Black/Yellow (BK/YE) wire that comes from fuse F1-11 (15 amp) in the Battery Junction Box (BJB). Check for power on the Yellow/White (YE/WH) wire from the 120 amp mega fuse in the BJB. If the 2 power wires check out OK, unplug the Light Green/Red (LG/R) that supplies the ground to the charge light on the dash and ground it to verify the light comes on. If the light does not come on, check fuse F2-16 (10 amp) for a blown or missing fuse. If the charge light stays on when the wire is disconnected, check the LG/R wire for a short to ground. If the light does go out when the LG/R wire is disconnected, replace the alternator.