I haven't found anything which lets me look further back than Thomas Gillikin (28 Aug 1778 Carteret will).I'm intrigued by your idea that there are two branches of the family, as I'd always considered all of the Carteret Gillikins to have descended from this Thomas.
The David Gillikin you're referring to could be descended from Charles (taxed in 1779 Carteret for 200 acres, 7 cows and 1 horse).Charles was named in the 1778 will, and seems to be one of Thomas' older sons.I think this David was the Private in Captain Nelson's Company, Robert's Regiment for the War of 1812-15.That would fit with Charles' 1790 census showing 3 males under 16.I can account for sons Charles Jr. (26 May 1795 Carteret marriage to Alice Gabriel) and maybe another son, but this still leaves a third born before 1790.Incidentally, how were you able to Determine David was the father of Asa (20 Dec 1828 Carteret marriage to Sarah "Salley" Gillikin)?
There is some indirect evidence that Thomas may have been of Henrico County, Virginia Colony.On 11 Sep 1746 he witnessed a power of attorney granted by Richard Ward Sr. to kinsman Richard Ward of Carteret Co., to sell land in Henrico Co., VA and collect debts.Reference Henrico Records Vol. 1744-48 p. 208 and William & Mary Quarterly Vol. V.Thomas and his son Thomas appear together on a 14 Jun 1747 Carteret muster roll.You indicated that there may be an earlier Thomas, although I know nothing about him.
Thomas may have had two wives, naming only his second wife Mary in the 1778 will.On 8 Sep 1755 Love P Gillikin witnessed a deed from Ephraim Chadwick to possible son Solomon Chadwick for all 280 acres remaining of the grantor's land.Reference Carteret deed book F, pp. 447-448.