I have a 8' x 8' garage wall w/vapor barrier on warm side attached to house. This wall has 2 vertical duct runs. It had 5/8x drywall with fire stops insulated with R13FG batts except on the 2 duct runs which had nothing except on each side of ducts.
Over the last 15 or so years since house was built this wall developed black mold on outside of drywall where the 2 duct runs existing floor to about 6 feet up.
After tearing the drywall out I discovered that the mold was a result of condensation caused by the two ducts not having any insulation over the ducts between the duct and drywall and to make it worse the duct was actually touching the drywall. The ducts did have FG insulation on each side between duct studs but nothing facing the garage. So 15 years of condensation of hot vs cold and vice verses caused the mold and continued to feed the mold in all seasons. I painted all the wood around the 2 duct runs with oil base paint and will put non-faced FG R13 insulation in the old wall and over the 2 duct runs.
I have decided to install another 2x4 wall with a 1/2" gap between old and new wall. I am installing kraft faced R13 FG on cold side of new wall. I am assuming this will create a dead air space between the old & new wall that will create a dead air space and hopefully eliminate any future condensation issues.
My question is: Should I install a plastic vapor barrier on the new wall even though the existing wall has a vapor barrier already installed on the warm side, or is my double wall solution both with R13 FG and a vapor barrier already installed on old wall on warm side already enough that have solved the condensation issue for the future?