Source: Ancestry.com Family Trees (accuracy not guaranteed)
Name: Jacob Buxton
Birth: 12 Feb 1774 - Washington, Pennsylvania, USA
Death: 20 Aug 1836 - Independence Twp, Washington Co, PA

Father: Jacob Buxton (1751-1836)
Mother: Hannah Young (1751-1842)

First Spouse: Mary Sparks (1768-1807)
Married: 1795
Together they had six children whom I believe were:
Mary Buxton 1796–1880
Sarah Buxton 1799–
Darius Buxton 1800–1881
James Buxton 1802–1879
Anne or Anna Buxton 1804–
Aaron Buxton 1807–1876

Second Spouse: Elizabeth Davis (1787-1871)
Married: December 1, 1807
Together they had fourteen children.
Children:
Aris (b. August 14, 1808 - 1810)
twin sister (b. August 14, 1808 - 1808?) - no recorded name is known (perhaps stillbirth)
Davis (b. April 28, 1810 - 1890)
Amos (b. December 4, 1811 - 1898)
Ezekiel (b. July 11, 1813 - 1813)
Ezra (b. November 15, 1814 - 1875)
Hannah (b. October 8, 1816 - 1900)
Friend (b. October 2, 1818 - 1882)
Rebecca (b. September 1, 1820 - 1902)
Hadden (b. April 7, 1822 - 1904)
Absalom (b. March 25, 1824 - 1865)
Amon (b. June 15, 1826 - 1832)
Elizabeth (b. May 27, 1828 - 1908)
Melissa (b. April 27, 1831 - 1884)

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I believe the following to be true:

A family document says, "Jacob Buxton died on Aug 20th, 1836, Aged 62 years 5 months 8 days."

His parents were Jacob and Hannah Buxton of Cross Creek County. He was the father of twenty children, six by the first wife and fourteen by the second.

He had a mill on Cross Creek, just over the state line in West Virginia. He was killed in a fall from his mill in 1836, just a few months after his father's death.

He and his first wife, Mary (Sparks) Buxton, are buried at Cross Creek, while his second wife, Elizabeth (Davis) Buxton, and several of their children are buried at Bethel Ridge.

Davis Buxton (1810) was a son. Martin Luther Buxton was a grandson. Bertha Buxton Barnes (1884-1872) was a great granddaughter. The Buxtons who lived in Independence Township are descendants of Jacob Buxton, Jr.

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Pennsylvania, Tax and Exoneration, 1768-1801
Name: Jacob Buxton
Year: 1787
Town or Ward: Hopewell
County: Washington
Archive Rollname: 341

1800 United States Federal Census
Name: Jacob Buxton
Home in 1800: Hopewell, Washington, Pennsylvania
Free White Persons - Males - Under 10: 1
Free White Persons - Males - 26 thru 44: 1
Free White Persons - Females - Under 10: 1
Free White Persons - Females - 26 thru 44: 1
Number of Household Members Under 16: 2
Number of Household Members Over 25: 2
Number of Household Members: 4

Millennium File
Name: Jacob Jr (Prob) Buxton
Birth Date: 1783
Birth Place: Washington Co, Pennsylvania, USA
Father: Jacob Buxton
Mother: Hannah

1820 United States Federal Census
Name: Jacob Buckston
Home in 1820: Wellsburg, Brooke, Virginia
Enumeration Date: August 7, 1820
Free White Persons - Males Under 10: 4
Free White Persons - Males 10 thru 15: 1
Free White Persons - Males 16 thru 18: 1
Free White Persons - Males 16 thru 25: 2
Free White Persons - Males 45 and over: 1
Free White Persons - Females Under 10: 1
Free White Persons - Females 10 thru 15: 1
Free White Persons - Females 26 thru 44: 1
Number of Persons - Eng. in Manufactures: 2
Free White Persons - Under 16: 7
Free White Persons - Over 25: 2
Total Free White Persons: 11
Total Persons - White, Slaves, Colored: 11

He fought in the Indian Wars.

"The American Indian Wars (or Indian Wars) is the collective name for the various armed conflicts fought by European governments and colonists, and later the United States government and American settlers, against various American Indian tribes. These conflicts occurred within the United States and Canada from the time of the earliest colonial settlements in the 17th century until the 1920s. The various Indian Wars resulted from a wide variety of sources, including cultural clashes, land disputes, and criminal acts committed on both sides. European powers and the colonies also enlisted Indian tribes to help them conduct warfare against one another's colonial settlement.
American Indians (1540–1924)
First Nations (1540–1924)
Inuit (1542–1924)
Aleut (1743–1924)
Yupik (1784–1924)
Métis (1799–1924)
Provisional Government of Saskatchewan (1885)
Spanish Empire Spanish Empire (1540–1821)
Kingdom of France (1540–1763)
Kingdom of England (1607–1707)
British Empire (1707–1907)
Dutch Empire (1614–1664)
Swedish Empire (1638–55)
Hudson's Bay Company (1670–1924)
Russian Empire (1741–1867)
United States of America (1776–1924)
Vermont Republic (1777–1791)
Republic of West Florida (1810)
Denmark Danish Empire (1814-1924)
Mexico (1821–1867)
Republic of Texas (1836–1846)
California Republic (1846)
Confederate States of America Confederate States of America (1861–1865)
Dominion of Canada (1867–1924)
Dominion of Newfoundland (1907-1924)
After the American Revolution, many conflicts were local to specific states or regions and frequently involved disputes over land use; some entailed cycles of violent reprisal. The British Royal Proclamation of 1763 included in the Constitution of Canada prohibited white settlers from taking the lands of indigenous peoples in Canada without signing a treaty with them. It continues to be the law in Canada today, and 11 Numbered Treaties covering most of the First Nations lands limited the number of such conflicts.

As white settlers spread westward after 1780, the size, duration, and intensity of armed conflicts increased between settlers and Indians. The climax came in the War of 1812, which resulted in the defeat of major Indian coalitions in the Midwest and the South, and conflict with settlers became much less common. Conflicts were resolved by treaty, often through sale or exchange of territory between the federal government and specific tribes. The Indian Removal Act of 1830 authorized the US government to enforce the Indian removal east of the Mississippi River to the other side of the sparsely populated American frontier. The policy of removal was eventually refined to relocate Indian tribes to specially designated and federally protected reservations."
Source: Wikipedia

We went to this cemetery to visit his grave and to photograph the stone. There has been damage, and some stones are in a pile. Caretakers are trying to reconstruct the area. For now, there is no marker for him.