The battery warning lamp is controlled by the Body Control Module[BCM]. In the diagrams down below I have included the description and operation of the BCM as well as the instructions on how to self test the instrument cluster warning systems controlled by the BCM and also the Instrument Cluster wiring diagrams as well for reference. Please go through these guides and get back to us with what you find out.
Images (Click to enlarge)
Saturday, February 8th, 2020 AT 8:21 PM