Sorry about the delay in responding.I can not find an Elisha Buckhalter (or Burkhalter) in Edgefield.My third great grandfather Daniel Burkhalter had a brother named Elias, son of John Buckhalter (sic), who lived in Edgefield until about 1810, at which time he moved to Georgia (Putnam County).This Elias was born abt 1787, Edgefield, died after 1860, Lauderdale County, Mississippi.The name Elias appears again, as Daniel named one of his sons Elias.
Elias had a couple of sons whose names are not known, born in Edgefield about 1814 and 1816.He also named a son John Fleming, as did his brother Daniel.It gets twisted keeping them apart, since they both grew up in Mississippi.
Some say that John's middle name is Francis, but there is no proof of that, to my knowledge.His will lists his wife's name as Anne (some say Marcus).
There were a gang of Buckhalter/Burckhalter/Burkhalters in Edgefield in the latter 18th and early 19th centuries.Most descended from Michael (1719-1807), and Anna Denzler (1726-1800+).Your Elisha may be descended from another of the Burckhalters, since 5 brothers all arrived at the same time with the Palatines coming from Germany/Switzerland, and all started out in the Savannah area, and moved to or through Edgefield.
I thought possibly John's brother Christian may have had a son with a name similar to Elisha, but no luck so far.If I come up with anything, I'll let you know.If you're interested in the Elias/John connection, let me know.