that condensation is forming on vent stack. Probably re caulking the stack is futile. I always use Butly Rubber caulking when repairing leaks. It seems to give more.
Go up on the roof and look around the area up hill from the stack and see if you see any shingles or nail pop ups showing there. If the stack and stack shield is leaking it would be on the up hill side. Make sure that the lead is tucked firmly down inside, yes inside the vent pipe also.
Just too hard of a question to answer without seeing the situation.