When Gad Elmer was born on August 31, 1760, in South Hadley, Massachusetts, his father, Samuel, was 27 and his mother, Elizabeth, was 30. He married Anna Phillips on November 28, 1782, in Ashfield, Massachusetts. They had 12 children in 21 years. He died on November 13, 1819, in Ashfield, Massachusetts, at the age of 59, and was buried there.
Quoting from the US Sons of the American Revolution Membership Application #48469: Gad Elmer enlisted as a private August 17th 1777, in Lieutenant Ephriam Jenning's company, Col. David Field's (Hampshire Co.) regiment, roll dated at Ashfield, Mass. His service consisted of an Expedition to the Northward at the time of the battle of Bennington. His actual service was only five days, he being honorably discharged Aug 21, 1777.
The following are references to the authorities for the above statement: Massachusetts Soldiers and Sailors in the Revolution, Vol. V, Page 323. 
Original data from volume 5, page 323: Elmer, Gad. Private, Lieut. Ephraim Jenning's co., Col. David Field's (Hampshire Co.) regiment.; enlisted Aug. 17, 1777; discharged Aug. 21, 1777; service, 5 days, on an expedition to the Northward at the time of the battle of Bennington. Roll dated Ashfield.
Paternal relationship is confirmed through Y-chromosome DNA testing. William Elmer and Robert Elmore match on 35 out of 37 markers thereby confirming their direct paternal lines back to their MRCA Edward Elmer
13 November 1819 • Ashfield, Franklin, Massachusetts, USA 
13 Nov 1819 • Baptist Corner Cemetery, Ashfield, Franklin, Massachusetts, USA 
1790 United States Federal Census; Year: 1790; Census Place: Buckland, Hampshire, Massachusetts; Series: M637; Roll: 4; Page: 125; Image: 146; Family History Library Film: 0568144.
Source Information: Ancestry.com. 1790 United States Federal Census [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2010. Images reproduced by FamilySearch.
Original data: First Census of the United States, 1790 (NARA microfilm publication M637, 12 rolls). Records of the Bureau of the Census, Record Group 29. National Archives, Washington, D.C.
Home in 1790 (City, County, State): Buckland, Hampshire, Massachusetts.
Free White Persons - Females - 16 thru 25: 1: Anna Elmer
Free White Persons - Females - 26 thru 44: 1: Anne Elmer
Number of Household Members Under 16: 6
Number of Household Members Over 25: 2
Number of Household Members: 9
NOTE: Gad is the only named person in this census, all of the others are presumed from other facts.
NOTE 2: This area is a bit convoluted. There are four sons that could fit in the younger group and two in the larger age group. There are three other Elmer families next to this one. I suspect some of the children may be swapped with other families. Elmore-505 23:48, 7 December 2016 (EST)
Gad Elmer; Birth Date, 31 Aug 1760; Birth Place, South Hadley, Massachusetts; Death Date, 13 Nov 1819; Death Place, Ashfield, Massachusetts; SAR Membership, 18469; Role, Ancestor; Application Date, 19 Mar 1907; Spouse, Anne Phillips; Children, Luther Elmer.
Gad Elmer; Birth Date, 31 Aug 1760; Birth Place, South Hadley, Massachusetts; Death Date, 13 Nov 1819; Death Place, Ashfield, Massachusetts; SAR Membership, 29007; Role, Ancestor; Application Date, 6 Oct 1916; Spouse, Anne Phillips; Children, Daniel Elmer.
Gad Elmer; Birth Date, 31 Aug 1760; Birth Place, South Hadley, Massachusetts; Death Date, 13 Nov 1819; Death Place, Ashfield, Massachusetts; SAR Membership, 30979; Role, Ancestor; Application Date, 14 Feb 1918; Spouse, Anna Phillips; Children, Cleon Elmer.
Gad Elmer; Birth Date, 31 Aug 1760; Birth Place, South Hadley, Massachusetts; Death Date, 13 Nov 1819; Death Place, Ashfield, Massachusetts; SAR Membership, 67332; Role, Ancestor; Application Date, 25 Jun 1946; Father, Samuel Elmer; Mother, Elizabeth Canfield; Spouse, Anna Phillips; Children, Daniel Elmer.
Page 18: 70. GAD ELMER, (Samuel, Hezekiah, Edward, Edward) born at South Hadley, Mass. Aug. 31, 1760; married Nov. 28, 1782, Anna Phillips, daughter of Richard and Ruth (Pitts) Phillips, born May 4, 1763, and died March 3, 1812. He was a blacksmith and lived in Ashfield, Mass., where he owned a farm and where he died Nov. 13, 1819. Both were buried in the Baptist graveyard in said town. Children all born in Ashfield.
CHILDREN. SIXTH GENERATION.
I. Anna, b. Sept. 23, 1783; d. Sept. 19, 1867. 215
II. Betsy, b. June 7, 1785; d. Nov. 27, 1870. 216
III. Daniel, b. May 4, 1787; d. Oct. 9, 1866. 217
IV. Philo, b. Mar. 5, 1789; d. Oct. 27, 1841. 218
V. Gad, b. Sept. 6, 1790; d. unm. 219
VI. Adolphus, b. Apr. 10, 1794: d. Aug. 1839 220
VII. Alpheus. b. Nov. 26, 1795; d. Apr. 28, 1867; unm. 221
VIII Almira. b. Jan. 25. 1798; d. d.. 222
IX. Luther b. Sept. 11, 1799; d. Apr. 7, 1857 223
X. A child, b. Jan. 8, 1801; without name 224
XI. Cleon, b. May 25, 1802; d. Feb. 27, 1878. 225
XII. Horace, b. Nov. 20, 1804; d. Feb. 26, 1854. 226
Original data: Dodd, Jordan, Liahona Research, comp. Massachusetts, Marriages, 1633-1850. With some noted exceptions all marriage records in this collection can be found at the Family History Library in Salt Lake City, Utah, and may be available through Family History Centers throughout the United States.
Gad Elmer; Gender, Male; Spouse, Anne Phillips; Marriage Date, 28 Nov 1782; City, Ashfield; County, Franklin; Source, Family History Library, Salt Lake City, UT, Film # 0902896.
Ancestry.com, Massachusetts Soldiers and Sailors in the Revolutionary War (Images Online) [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2004.
Original data: Massachusetts. Secretary of the Commonwealth. Massachusetts Soldiers and Sailors of the Revolutionary War. Vol. 1-17. Boston, MA, USA: Wright & Potter Printing, 1896-1908. About Massachusetts Soldiers and Sailors in the Revolutionary War (Images Online)
Information: Prepared by the Secretary of the Commonwealth, this is an indexed compilation of the records of the Massachusetts soldiers and sailors who served in the army or navy during the Revolutionary War. The work is a 17 volume series that contains an alphabetized list of all surnames. The records in this database give, when available, the name and age of the individual, town of residence, rank, the date and location of enlistment, areas and length of service, date of discharge, and a description of the individual's physical features.
It may be possible to confirm family relationships with Gad by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree: