Martin Brimmer is not in my direct Brimmer line, as far as I can prove, but I did research him while looking for my Brimmer ancestors.
Martin Brimmer is mentioned in about twenty volumes of New England Historic Genealogical Register, from Volume 1 in 1847 to Vol 143 in 1989. I found nothing about a connection to "T-Wharf", but the volumes have a wealth of genealogical information about several generations of Martin Brimmers. Some have marriages, some have children, some have deaths. His term as Mayor of Boston is mentioned in at least one volume. In a February 1730 petition, Martin Brimmer terms himself, " a protestant German came over from Hanover." (NEHGR Vol 13, p. 316)