There were a bunch of Gilmore marriages (various spellings), mostly female c. 1815 - the only earlier Gilmore is Alexander m Mary Taylor in 1756 but it would appear none of that family are buried or left a will on the Island(they probably left at revestment).

Your two names are somewhat Scottish - there might be a clue in the marriage reg, other than that wills ? or possibly MI's ? though those in Santan appear to offer no clue.