Rachel Gibson was born 1717, it is said in Rapidan, Virginia,  which at that time lay in either King William or King and Queen County, Virginia. She died 19 Feb 1761 at her home Midland in Orange County, Virginia (formed in 1734 from Spotsylvania County).
Rachel's parents were Jonathan Gibson Jr./II (c.1700-1745) and Margaret Catlett (c.1700-c.1750). A number of online genealogies show Rachel as the daughter of Jonathan Gibson Sr./I and Elizabeth Thornton, but even though they too had a daughter named Rachel, she was not the one who married George Taylor.
Notes in the Filson Club file associated with the diary of Rachel's fifth son Francis Taylor (1747-1799) clearly state that George Taylor's wife Rachel Gibson was the daughter of the Jonathan Gibson who was one of the earliest clerks of the court of Orange Co. (formed in 1734); who died in 1745 "from accidental poison in the prime of his life;" and who was married to Margaret Catlett.
Rachel's father could not have been Jonathan Gibson Sr./I, since his will is dated 1727 in King George Co. and he is reported to have died in about 1729 in King George Co., which at the age of about 60 cannot be considered to be in "the prime of his life."
The notes in the Filson Club file are corroborated in the Kentucky State Historical Society Register and by William Kyle Anderson's book.
The Jonathan Gibson Jr./II (c. 1700-1745) of Orange Co., apparently died in testate - there was no will on file for him in Orange Co., but there are two inventories & appraisals on file for his estate, and "Margaret" is named as the administrator of both - one dated 06 Mar 1745 and one dated 27 Jun 1745.
This same Jonathan Gibson appears to be confirmed as the son of the Jonathan Gibson who was married to Elizabeth Thornton by the mention in the inventory of his estate of a slave "Caesar" who was willed to Jonathan Jr. by his father Jonathan Gibson Sr./I who died after 1727.
Several un-sourced dates for Jonathan Gibson and Elizabeth Thornton's daughter Rachel's birth date appear as "about 1705" or "about 1706," which tracks with their other three children who are all shown as born before 1710-11.
The confusion between these two Rachels is understandable since it is certainly possible (though not likely) that JG & ET had a daughter born in 1717 when they were about 47 and 44, respectively; and by the fact that their daughter Rachel appears to have still been un-wed in 1732 when her mother Elizabeth's will was made in 1732.
Rachel and George Taylor were married 28 Feb 1738 in Orange Co., and their 11 children - all sons - were: 
James, b. 16 Dec 1738, m. Ann Pendleton, d. 1799 in Jefferson Co., KY
George, b. 08 Jan 1741, d. 20 Feb 1761 from smallpox contracted in the French-Indian War
Jonathan, b. 03 Dec 1742, m. Ann Berry, d. 1804 in Clark Co., KY
Edmund, b. 21 Oct 1744, m. Sarah Stubbs, d. 01 Jul 1786 in Jefferson Co., KY
Francis, b. 09 Mar 1747, never married, d. Nov 1799 in Orange Co., VA
Richard, b. 06 Jan 1749, m. Catherine Davis, d. 30 Aug 1825 in Oldham Co., KY
John, b. 27 Jan 1751, d. 1781 in the British prison ship Jersey in New York harbor
William, b. 23 Jan 1753, m1. Lucy Hord, m2. Elizabeth Coats, d. 14 Apr 1830 in Jefferson Co., KY
Charles, b. 03 Jan 1755, m. his step-sister Sarah Conway, d. abt. 1805
Reuben, b. 14 Jan 1757, m. Rebecca Moore, d. 30 Nov 1824 in Jefferson Co., KY
From Jouett Taylor Prisley's family history and genealogy papers:
Two small relics of the Gibson family were passed down to Taylor descendants -- two small silver spoons, well bitten and bent by generations of teething babies, always referred to in the Taylor family as “the Gibson spoons.”
Rachel was 20 when she married George Taylor, who was then 27.
Rachel died from smallpox, contracted from her second son George, who reportedly brought it home from the French and Indian Wars. Refusing to leave the nursing to the slaves, Rachel became infected and followed her 20-year-old son in death by two weeks. She was 43, leaving of her ten surviving sons: three young adults, and seven in an age spread from 14 to under two years.
↑ Taylor family historians: 1) Dr. Andrew Glassell Grinnan, onetime owner of the diary and great-grandson of Erasmus Taylor; 2) William Kyle Anderson, descendant of Commodore Richard Taylor; and 3) Philip Fall Taylor (1864-1916)
↑ King George Co. Will Book A-1, 1721-1752, Pages 82-83
↑ Article by Alice Elizabeth Trabue, Register of the Kentucky State Historical Society, Volume 18, Issue 54, Kentucky State Historical Society, 1918, page 28
↑ Donald Robertson and his wife Rachel Rogers of King and Queen County, Virginia: their ancestry and posterity: also a brief account of the ancestry of Commodore Richard Taylor of Orange County, Virginia, and his naval history during the War of the American Revolution. Anderson, William Kyle, Detroit, Winn & Hammond, printers, 1900, pg. 238
It may be possible to confirm family relationships with Rachel 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 DNA with Rachel: