2006 Chevy Trailblazer Loss in voltage

We have owned a trailblazer for 3 years now sfter we bought it gently used with 12000 miles on it. Other than the fuel level sensor going bad twice it has been a very reliable car for the wife to drive everyday. The problem I am having now is driving me insane! The lights constantly go from dim to bright and back to dim but only when stopped. You can see the volt gauge go from 14.5 down to 12 with the lights doing their thing. I have changed the alternator, checked and rechecked the wiring to the alternator, and installed a brand new battery from auto zone. I am at a complete loss as to what to do next. Is this a common issue with these trailblazers?