Notes:

Genealogy of the Miller and Pursel Families has her name as Elizabeth Garritzen.

Elizabeth Gerritsen Britton, Brouwer
BIRTH 1 May 1681 Brooklyn, Kings County (Brooklyn), New York, USA
DEATH unknown Dongan Hills, Richmond County (Staten Island), New York, USA
BURIAL Saint Andrews Church Cemetery Richmondtown, Richmond County (Staten Island), New York

Daughter of Jan Gerritszen and Elisabeth Gysberts.
William J. Hoffman, "Brouwer Beginnings; The First Three Generations of the Adam Brouwer Berchoven Family", The American Genealogist 23:193-206; 24:23-32, 96-102, 161-170 (1947, 1948).
Elmer Garfield Van Name, Britton Genealogy: Early Generations from Somerset, England to Staten Island, New York (Woodbury, New Jersey: Gloucester County Historical Society, 1970), p.6.
Phylis J. Miller, "The Garrison-Gerritsen Descendants of Gerrit Jansen Van Oldenburg Alias Gerrit de Moe", New York Genealogical and Biographical Record Vol. 124, pp.1-9 (Jan 1993).

Married 1st before April 1714 Nathaniel Britton, son of Nathaniel Britton and Ann Stillwell.
Elmer Garfield Van Name, Britton Genealogy: Early Generations from Somerset, England to Staten Island, New York (Woodbury, New Jersey: Gloucester County Historical Society, 1970), p.6.

Her husband, Nathaniel Britton, administered the estate of her brother Cornelis Garretson of Richmond County on 15 April 1714.
Phylis J. Miller, "The Garrison-Gerritsen Descendants of Gerrit Jansen Van Oldenburg Alias Gerrit de Moe", New York Genealogical and Biographical Record Vol. 124, pp.1-9 (Jan 1993).

On 1 Sep 1732, an agreement was made between Abraham Brouwer, of Brooklyn, miller and Elizabeth Brittaine, widow of Nathaniel, late of Staten Island, wherein it was set forth that they intended to marry, and it was agreed that Abraham Brouwer should pay her 200 pounds per year so long as she remained his widow, which should be in lieu of dower. "If she should marry again this allowance is revoked" (recorded 16 Apr 1739, liber V, p.95, Kings Co. Records).
Kings County (New York) Conveyances, Deeds v. 5-7; film #1413190 (Salt Lake City, Utah: Filmed by the Genealogical Society of Utah, 1957, 1958, 1990), Microfilm of the original records at the New York Registers Office, New York City, v.5, p.95.

Elizabeth Gerritsen married second circa 1732 Abraham Brouwer, son of Adam Brouwer and Magdalena Jacobs Verdon.
William J. Hoffman, "Brouwer Beginnings; The First Three Generations of the Adam Brouwer Berchoven Family", The American Genealogist 23:193-206; 24:23-32, 96-102, 161-170 (1947, 1948).
Elmer Garfield Van Name, Britton Genealogy: Early Generations from Somerset, England to Staten Island, New York (Woodbury, New Jersey: Gloucester County Historical Society, 1970), p.9.

Witnessed the baptism of Abraham Brouwer , son of Abraham Brouwer and Sara Kimber, on 18 February 1739 at Reformed Protestant Dutch Church, New Utrecht, Kings Co., Long Island, New York, (sponsors Abraham Brouwer and Elizabeth z.h.v.).
"Records of the Reformed Church of New Utrecht, Long Island", New York Genealogical and Biographical Record Vol.112-113 (1981-1982): 113 (1982):76. Abraham; parents: Abraham Brouwer, Jr., Sara, s.v..

Elizabeth Gerritsen was living on 30 November 1743; when she consented to the marriage of her son, William Britton.
Elmer Garfield Van Name, Britton Genealogy: Early Generations from Somerset, England to Staten Island, New York (Woodbury, New Jersey: Gloucester County Historical Society, 1970), p.9.

Bio includes data from The Brouwer Genealogy Database.
http://freepages.genealogy.rootsweb.ancestry.com/~brouwergenealogydata/surname_index.htm

https://www.wikitree.com/wiki/Gerritsen-185
Biography Elizabeth was born 1 May 1681 in Brooklyn, Kings, New York.[1][2]

After Nathaniel's death, Elizabeth married Abraham Brouwer (Brewer) of Brooklyn. As Elizabeth Brewer, she signs William's marriage request.

Sources
findagrave.com
Phyllis J. Miller, p, 5. Phyllis J. Miller, "Garrison-Gerritsen Descendants of Gerrit Jansen Van Oldenburg alias Gerrit De Mof" New York Genealogical and Biographical Record, January 1993, Vol. 124, Number 1, p. 5.
findagrave.com, http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=48527910 (give the exact date).
Chester, Chris. "The Brouwer Genealogy Database." freepages.genealogy.rootsweb.ancestry.com/~brouwergenealogydata. Accessed 03 Aug 2017. http://freepages.genealogy.rootsweb.ancestry.com/~brouwergenealogydata/index.htm Elizabeth Gerritsen

Buried:
https://www.findagrave.com/memorial/48527910/elizabeth-brouwer

Family/Spouse: Nathaniel Brittain. Nathaniel (son of Nathaniel Brittain and Ann Stillwell) was born in 1662 in Staten Island, Richmond County, NY; died about 11 Nov 1729 in Staten Island, Richmond County, NY; was buried in Saint Andrews Church Cemetery, Richmondtown, Richmond County, NY. [Group Sheet] [Family Chart]

1. Rachel Brittain
2. Sarah Brittain
3. Samuel Brittain
4. Mary Brittain
5. William Brittain was born in 1725 in Staten Island, New York; died on 15 Mar 1804 in Upper Mt. Bethel Township, Northampton County, PA; was buried in Saint Andrews Church Cemetery, Richmondtown, Richmond County, NY.

Notes:

https://www.findagrave.com/memorial/176420098/jan-gerritszen
Jan Gerritszen
BIRTH 4 May 1642
DEATH unknown
BURIAL Non-Cemetery Burial, Specifically: location of grave unknown

Son of Gerrit Janszen van Oldenburg and Clara Matthys.
"Records of the Reformed Dutch Church in New York", New York Genealogical and Biographical Record Vols.5- (1874-): 5:31.
Perry Streeter, "Gerrit Jansen van Oldenburg: DNA Testing Yields More Garrison Descendants in New Jersey & New York", New Netherland Connections Vol. 15, page 16 (2010): 15:17.
Phylis J. Miller, "The Garrison-Gerritsen Descendants of Gerrit Jansen Van Oldenburg Alias Gerrit de Moe", New York Genealogical and Biographical Record Vol. 124, pp.1-9 (Jan 1993).

Baptized on 4 May 1642 at Reformed Dutch Church, New Amsterdam, sponsors Jan Janszen dam, olof Stephenszen Van Courtlt., Elsje Jan Pieterszen.
"Records of the Reformed Dutch Church in New York", New York Genealogical and Biographical Record Vols.5- (1874-): 5:31. Jan; parents: Gerrt. Janszen, Oldenburgh; witnesses: Jan Janszen dam, olof Stephenszen Van Courtlt., Elsje Jan Pieterszens.

Married Elisabeth Gysberts, daughter of Gysbert Theuniszen van Barneveldt and Aeltje Wouters, "say 1676" according to one published source, but possibly as early as 1670 or earlier as argued by another.
Phylis J. Miller, "The Garrison-Gerritsen Descendants of Gerrit Jansen Van Oldenburg Alias Gerrit de Moe", New York Genealogical and Biographical Record Vol. 124, pp.1-9 (Jan 1993): Married say 1676 based upon an estimated birth date of eldest son.
Perry Streeter, "Gerrit Jansen van Oldenburg: DNA Testing Yields More Garrison Descendants in New Jersey & New York", New Netherland Connections Vol. 15, page 16 (2010): 15:17. Argues for an earlier marriage date then 1676.

He received a patent for 24 morgens of land at New Utrecht on 16 Jan 1662.
Phylis J. Miller, "The Garrison-Gerritsen Descendants of Gerrit Jansen Van Oldenburg Alias Gerrit de Moe", New York Genealogical and Biographical Record Vol. 124, pp.1-9 (Jan 1993).

On 1 Nov 1675 John Garretsn was granted a patent for lands on Long Neck upon Staten Island. A survey of 80 acres on Long Neck was laid out for Jon Garrison in early 1676. Another survey for 161 acres laid out for John Garrats De Muff, was made in March 1686. He was named tax commissioner on Staten Island in 1681. On 14 March 1691 he was given power of attorney by his brother Jacob Garrottsone to sell land on Staten Island, and John sold it on 17 Aug 1692.
Ibid.

Children by Elisabeth Gysberts:
Johannes Gerritsen b. ca. 1671
Jacob Gerritsen b. 30 May 1680, d. before May 1700
Cornelis Gerritsen b. ca. 1682, d. before 15 Apr 1714
Aeltie Gerritsen b. ca. 1685, d. before Jan 1742/43
Elizabeth Gerritsen b. ca. 1688
Ibid.

Jan Gerritszen died before March 1697.
Ibid.

Bio includes data from The Brouwer Genealogy Database.
http://freepages.genealogy.rootsweb.ancestry.com/~brouwergenealogydata/surname_index.htm

Jan married Elisabeth Gysberts. Elisabeth was born in 1660 in New York; died in 1703 in Staten Island, New York. [Group Sheet] [Family Chart]

Notes:

https://www.findagrave.com/memorial/177574124/elisabeth-gysberts
Elisabeth Gysberts
BIRTH unknown
DEATH 1703
BURIAL Non-Cemetery Burial, Specifically: location of grave unknown

Probable daughter of Gysbert Theuniszen van Barneveldt and Aeltje Wouters.
Phylis J. Miller, "The Garrison-Gerritsen Descendants of Gerrit Jansen Van Oldenburg Alias Gerrit de Moe", New York Genealogical and Biographical Record Vol. 124, pp.1-9 (Jan 1993).
Perry Streeter, "Gerrit Jansen van Oldenburg: DNA Testing Yields More Garrison Descendants in New Jersey & New York", New Netherland Connections Vol. 15, page 16 (2010): 15:17. Possibly the unkown fourth child identified in 1659 (NYGBR 124 (1993): Macy, "The Verschuer Family of Bushwick".

Elisabeth Gysberts was probably born between 1645 and 1655.

She married Jan Gerritszen, son of Gerrit Janszen van Oldenburg and Clara Matthys, "say 1676" according to one published source, but possibly as early as 1670 or earlier as argued by another.
Phylis J. Miller, "The Garrison-Gerritsen Descendants of Gerrit Jansen Van Oldenburg Alias Gerrit de Moe", New York Genealogical and Biographical Record Vol. 124, pp.1-9 (Jan 1993): Married say 1676 based upon an estimated birth date of eldest son.
Perry Streeter, "Gerrit Jansen van Oldenburg: DNA Testing Yields More Garrison Descendants in New Jersey & New York", New Netherland Connections Vol. 15, page 16 (2010): 15:17. Argues for an earlier marriage date then 1676.

As a widow of John Garritse, called "Elisabeth garritse vande haes," she bought 178 acres at the "head of Fresh Kill" from Vincent Fountaine in March 1697. She sold half of this land to Pierre Joubert on 22 May 1699.
Phylis J. Miller, "The Garrison-Gerritsen Descendants of Gerrit Jansen Van Oldenburg Alias Gerrit de Moe", New York Genealogical and Biographical Record Vol. 124, pp.1-9 (Jan 1993).

Elisabeth Gysberts died circa 1703; (in Jan 1704 her son, Johannes Garrison, sold the land on which she lived).
Ibid.

Bio includes data from The Brouwer Genealogy Database.
http://freepages.genealogy.rootsweb.ancestry.com/~brouwergenealogydata/surname_index.htm