She is listed in her daughters death record as Mary A. Gaston.
Names as they appear in Daughters Death Record, click for larger Image.
A family tree by hjlawson on Ancestry.com says she was born in Edinburgh, Scotland.
Son - Moses, b 1819 in Pugwash, Cumberland County, Nova Scotia Moses profile on Geni. Moses GASTON was born around 1819 in Pugwash, Nova Scotia, Canada, the son of William and Mary Molly (Redmond) GASTON. Moses' parents were born in Ireland, so Moses was first-generation Canadian.
Shipwreck off Nova Scotia in 1818 - The Frame? Geni The "Acadian", a Halifax weekly paper, reported on October 10, 1818; "The Brig "Fame" (The Master being; Captain James Hardy) from Belfast, Ireland, for this place, out 49 days with 114 passengers went on shore Sunday (02/Oct/1818) about 11:00 o'clock at Cole Harbour. Passengers and crew saved."
The following is from a private message from C. Kellett to me on 3 Dec 2017:
William Gaston was (b) ~1792 Ireland, (m) Mary Margaret Redmond, aka Molly Redmond (b) ~1796 No. Ireland, (d) 6/11/1875. My understanding was that Mary was a desc. of Lady Betty Redmond. They lived one mile out Sheet Harbor Rd. in Musquodoboit, NS.
Parents of Mary Redman were Moses Redman (The Redman name took on various spellings as time went on) (b) ~1770 Carrickfergus, Ireland (m) Rebecca Dunn of Ireland (b) ~1773-75. (m) 1791. He died 12/2/1849 River John, NS. She (d) River John, NS, same date. They had 13 children. From County Antrim, Ireland they sailed in 1818 on the Brig "Fame" which sank off Newfoundland. I do not have the parents of William Gaston Sr.
Children of William & Mary Gaston were: John (b) 1819 Carrickfergus, Ire. and (m) Marjorie Jean Blackie (b) 1822 Ire. Both died in Chaplin, NS. Andrew (b) ~1820-25, Carrickfergus, Ire., (m) Susan Kirk Dean in 184., She was (b) 2/27/1822. Moses (b) ~1821 of Pugwash, NS, (m) Anne McDonald, and Mary A. (b) ~1831 Popes Harbor, NS, (m) John H. Lorman of NS on 12/29/1851 by Rev. J. Martin. John Lorman (d) at the age of 100 in Lowell, MA on 1/26/1918. Mary (d) 5/27/1886.
I'm taking the death date to the profile even though it's unsourced for now. Hopefully C. will help and add more. Whitten-1 09:26, 7 December 2017 (EST)
Middle name is listed as Margaret in a list of children included in an Ancestry.com Post (which has been copied numerous times to numerous sites) 
↑ "Massachusetts Deaths, 1841-1915," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:N75V-NNS : accessed 27 January 2016), John H. Lorman in entry for Mary A. Lorman, 27 May 1886; citing Lowell, Massachusetts, v 374 p 123, State Archives, Boston; FHL microfilm 960,232.
↑ Redmond / Redman Family Reunion -- August 16 and 17, 2002 -- Nova Scotia, Canada, by R.W. Rick Redmond, Fri, 11 Jan 2002. 
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It may be possible to confirm family relationships with Mary by comparing test results with other carriers of her mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage (beta) of DNA with Mary: