Problem is all 120vac related. Not 12vdc or convertor. I would bet failing neutral circuit. Use vom multimeter at transfer switch input neutral and each hot leg. Be patient as your eyes have to stay focus on digital meter voltage for voltage blip, and someone else to watch 120vac lights for flicker. If flicker occurs but meter stays constant then measure on output side of transfer switch and note results. If meter registers blip in voltage on output side of transfer switch when lights flicker but not on input side its your transfer switch. If your meter has setting for peak that would help as you won't have to baby sit it so much. My bet is failing neutral within transfer switch!!