The cap area of the chimney presents such a small area to collect rainfall that it seems to me (unqualified that I am in this area to offer an opinion, but it hasn't stopped me before) unlikely to be the source of a large quantity of water. The roof, however, would intercept a lot of water and if your gutters were clogged the water might dam at the flashing of the brick chimney and find an entry point. Are your downspouts showing restricted water flow when it rains? Any water coming in the attic?

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1985 300D Turbo
"Evolution is God's way of giving upgrades" Francis Collins