That was Sarah Falconer Graham, not Sarah Falconer. The full record reads, "John Taylor Esquire a Captain in the Military Service of the United Company of Merchants of England trading to the East Indies on their Bengal Establishment a Bachelor and Miss Sarah Falconer Graham of Bombay Spinster were married in this Church by Licence from the Honourable the Court of the Recorder, this seventeenth day of July in the year of our Lord One Thousand Eight hundred and twenty three by Me, Thos Carr, Garrison Chaplain. This marriage was solemnized between us, J Taylor, Sarah Falconer Graham, in the presence of us, Henrietta Louiza Wedderburn, Jane Black, J Wedderburn, Chas Thomas, Wm Bruce."
The family of John Taylor and Sarah Falconer were born between 1780 and 1795. Sarah Falconer Graham, daughter of William Graham and Janet Edmonstone, was born in 1799. Her baptism is in the registers of both Dirleton and Haddington.
So this is a completely different couple.
Though her unusual given names may warrant some investigation. William Graham and Janet Edmonstone were married in Haddington in 1796. Could Janet be the daughter of Andrew Edmonstone and Mary Falconer, baptised in Lauder in 1771? Could Mary be connected to Thomas Falconer of Reidhall/Woodcote?