Note 1: My reading of Rachel's gravestone birth date was 1 or 4 July 1797; someone else listed the day as 17 July, possibly from reading the legend on the stone itself. The lister didn't record a birth year.
Note 2: I am unable to read any of the engraving on the gravestone posted to Find a Grave as being hers. The notes accompanying it state that the person is Elizabeth Elliot, wife of William Elliot and daughter of William Rust and Rachel Alexander. Birth and death dates given are 20 April 1821 and 29 November 1848. I cannot vouch for any of the data. She is buried in the Rust Family Cemetery, but William Elliot, who survived her by many years, is buried elsewhere.
Rachel was dead before Tate made his will in 1837, and neither she nor her husband William Rust are mentioned in the will.
Sarah: her gravestone inscription lists her by maiden name and married to Jos R Rust. Both are buried in the Rust Family Cemetery.
William Rust was probably a brother of Joseph Rust, who was married to Rachel's sister Catherine. Note also that William and Rachel named a son Joseph.
Note 1: I cannot read inscriptions from the photo on Find a Grave and know from other sources only that he died in 1845; however, the posted information is that he was born 25 August 1789 and died 5 February 1845.