Don, After I posted to you that I did not know if my Willem Brouwer/Brewer was ever in NJ, I recalled that all of the children of Pieter Brouwer of Flatlands moved to New Jersey in the 1720's, so it is very likely that Willem moved there too and there may well be a connection between the William Brewer who died 1729 and my Willem Brouwer/Brewer, son of Pieter Brouwer.
As far as a connection between Chambers and Brewer, it is quite interesting to note that my ancestor John Brewer (b April 1768 in Readington, Hunterdon Co, NJ) and one William Chambers were the first settlers of Genesee (now Niagara Co) wilderness at 18 mile creek (now Orcott, Niagara Co, NY) in 1807 and they both arrived there together from Grimsby town, Canada. There was a large influx of people from New Jersey in 1784 to 1790's to Grimsby.In the records of Grimsby, Canada there was a list of burials that included in July 1794 "a child of a poor stranger called Chambers" and on October 7 the wife of James Chambers, followed on the 21st by "James Chambers, an unfortunate stranger."I haven't been able to establish if William Chambers was related to this James Chambers, but I assume he was.William Chambers and John Brewer were close neighbors and pioneers at 18 mile creek, Genesee (Niagara) until Chambers died in 1825 attempting to cross the Niagara River above the falls in a skiff.
I don't quite get the connection you wrote of with regard to ---"James' wife was Phebe, and I have never been able to find what her maiden name was. So, I thought perhaps she was a Brewer as there was a John Chambers, Jr. who owned land in Amwell Twp. and sold it to Francis Quick in 1724."From that information, what leads you to think Phebe's name may have been Brewer given only that there was a James Chambers jr and sold some property? Just the probability that the Chambers and Brewers were close given that James was administrator to Brewers estate?
Did any of your Chambers family move from NJ to Canada?If so, we may have an interesting connection.