My Fender Showmaster Celtic H has a single Atomic II humbucker at the bridge. I was thinking of adding a push-pull pot to either cut one of the coils or put both coils in parallel. Of the two, which would you folks recommend? That pickup is quite hot and aggressive, so either method would give me some nice tonal options.

From what I've read, the pickup is supposed to have green, red, black, and white leads. Mine has two black (one is thicker than the other), white and green. Green is hot, the thicker black one is ground, and the white and black are taped together. If the standard wiring on this page is correct, should I just treat the thicker black lead as if it were the red one and go from there?