Hi again - just had a quick look at my notes again and have found the following:
Elizabeth Rymer's father was William Rymer and her mother appears to be Martha Faulds born Aug 1782, Old Monkland. She died in 1804 in Spanish Town, Tortola. Martha's father was Andrew Faulds and her mother was Martha Down. Several members of the Faulds and Rymer families intermarried and Andrew Faulds and John Rymer Snr had business interests together (found this through some court case records).