Hello. Are you aware that there are probate records for a John Groom at the familysearch.org website that fits nearly everything you mentioned except that he was the brother of Lawrence Groom of Bridgeport not his uncle? (see below)
Register at the familysearch.org website, sign in, navigate to the "Kings County Estate Files" and you can view the records for yourself.
It shows John Groom died in the hospital on Blackwell Island, NY, intestate, Apr 9, 1915, previous residence was 431 39th St., Brooklyn and that his only surviving kin were: brother (the petitioner): Lawrence Groom of 460 Nichol Ave., Bridgeport CT nephew: James Groom, 43139th St., Brooklyn nephew: John Groom, 43139th St., Brooklyn nephew: Leo Groom, 279 Amberland St., Brooklyn nephew: William Groom, 4414th Ave., Brooklyn nephew : Lawrence Groom, 781Bergen St., Brooklyn niece: Annie Groom, 43139th St., Brooklyn niece: Marion Campbell, 4124th Ave., Brooklyn
As you can see, most of the nieces and nephews are the ones you listed as the children of Patrick Groom therefore it appears that Patrick and John WERE brothers and they had a brother Lawrence who lived in Bridgeport.
Also, have you seen these Brooklyn City directory entries? 1882 Groom Patrick, hostler, 612 Bergen 1884 Groom Patrick, livery, 612 Bergen 1885 Groom Patrick, laborer, 250 St Mark's av 1886 not in there 1887 Groom Ellen, wid of Patrick, 784 Dean 1887 Groom Roger, hostler, 784 Dean
Was Roger Groom another brother?
Since the Brooklyn directory corrections usually began about the month of May of the previous year of publication, Patrick may have died as early as May 1884.
As you must already know, in the 1880 census Patrick is shown to be residing at 612 Bergen with wife Ellen and most of the children you listed in your query.