Unattached Arkansas Fulkersons

We begin with a serendipitous find from several years back - four unknown Fulkersons interred in an old Conway County, Arkansas cemetery:

Martinville Cemetery: James Adam Fulkerson (29 Sep 1888 to 7 Aug 1968); Joseph Edd Fulkerson (20 May 1884 to 19 Feb 1978); Louisa J. Fulkerson (1 Nov 1853 to 7 Jul 1914), double stone with William T. Fulkerson (5 Nov 1842 to 4 Jan 1917).

We know of a William T. FULKERSON from this site's previous Civil War research:
"Pvt. William Thomas FULKERSON, Co. A, 10th Regiment, Arkansas Cavalry (Confederate) from Van Buren, Arkansas. He was a prisoner at Rock Island, IL, from which he enlisted in the 3rd US Volunteer Infantry on 15 Oct 1864 and was sent to protect Western settlements against Indian attack as a 'Galvanized Yankee.' He received a pension for his Union service."

From LYNN/LINN family research, we learn that his wife Louisa was Louisa Jane LYNN/LINN of Morganton, Van Buren Co., AR, dau of William LYNN/LINN and Intha PATTERSON, both of whom were originally from Tennessee. The same research tells us that James Adam and Joseph (Edward) were her sons:
"14. LOUISA JANE3 LYNN/LINN (WILLIAM2, ASA1) was born 01 Nov 1853 in Morganton, Van Buren Co., AR, and died 07 Jul 1913 in Martinville, AR. She married WILLIAM TOM FULKERSON, son of JOHN FULKERSON and NANCY. He was born 05 Nov 1842 in TN, and died 04 Jan 1917 in Martinville, AR.