Any auto parts store will test the battery and alternator for free.
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OK so the alternator is probably charging but that says nothing about whether the battery is good or bad. It needs a load test and a multimeter isn't the answer for that. Have the battery tested.I was getting 14.6 v with multimeter hooked up to battery with Tahoe running.
also check the abs relay. pretty much my issue on my 05 denaliI have a 03 Tahoe and had the same problem I’m also was a GM mechanic for 10 years ...I replaced my battery and yes my gauge cluster was bad the gauges worked when they wanted to after replacing my battery cables to do the big 3 I found that the cluster was to blame I had a buddy at work look up the tech notes and the cluster when bad creates a parasitic draw and weak batteries have no chance