Sounds like a needle and seat issue. It may be stuck so gas is just trickling into the bowl. And when it sits long enough the bowl fills up and then it will start and run until the bowl goes dry again. Old gas can create vanish when it evaporates and it is very sticky stuff. Did you soak the whole carb in cleaner when you did the rebuild. Some of the small holes or venturi's can get clogged as well.