Father is assumed to be an Archibald from naming pattern - eldest known/believed son is an Archibald
yDNA matching confirms his connection to John and Bessie (Flint) Fairbairn's family
He is a different Archibald from the son of Robert Fairbairn & Agnes Landreth (as that Archibald married Mary Grierson), so belongs to another line down from John - although technically it could also be from a sibling or other relative of John's.
This latter option would be pushing the limits to explain the number of autosomal DNA matches we have between the (presumed) descendants of John and Bessie though. Henderson-2297 22:30, 3 August 2017 (EDT)
↑ Source #S1: Bap. (at Morebattle) 23 Feb 1800 David s/o Archd FAIRBAIRN & Allison CROSSER, of Cavers, Par. of Eckford, ROX
Source S1 Morebattle, Gateshaw Session Records 1775-1907 (FHL Film: British #889486)
WikiTree profile Fairbairn-29 created through the import of HENDERSONLornaAncestorsPlus1Desc4WikiTree.ged on Oct 18, 2011 by L Henderson.
It may be possible to confirm family relationships with Archibald 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: