During my researches into ‘Brockett’ and its variants in records here in the UK from the 13th century onwards, I have not once come across any confusion between Brockett and Brackett. This has led me to the view that the two names are distinct and unrelated. They certainly have different original meanings. This is not of course to say that there was not a confusion in Connecticut in the 1780s in the case of your Christopher. In a Cambridgeshire village a local pronunciation of 'Brockett' early last century was more like 'Brackett' and I expect certain American regional accents tend or tended towards a ‘Brackett’ sound. Perhaps the CT census enumerator heard the name in such a way and wrote it down as he heard it? I would guess, however, that this was a unique mistake. Do you think so too?