Since then, I have noticed water a few more times, most obviously at the joint between the furnace and the hot air plenum.
The question is...where is the water coming from? I thought it might be running down the flue, so I had a look and sure enough there is a 1/8" gap between the flashing and the flue as it exits the chimney so I caulked it. But why hasn't this been a problem before?
Also, the flue is actually connected to the furnace below where I saw the water, so it didn't really make sense that the water was running down the flue.
While I'm at it, my furnace does not seem to have any sort of connection to the outside for combustion air (it is about 18 years old). Is it possible that the gap I caulked was to draw combustion air down the chimney between the liner and the flue?