I have found a Henry Fyge Jauncey online. He was in the Royal Navy, not sure if there's a connection anywhere. He died in the early 1820s and was born in the late 1780s.
Given that Gershom RAWLINS' will was proved in 1757, I wonder if you need to be looking at earlier dates?
According to the National Burial Index, the Rev. Fyge JAUNCEY was aged 75 at burial on 23 May 1812 at Castle Camps, Cambridgeshire, so born about 1736/7. He apparently married Helen ('Nelly') WHITE, known as the 'Belle of Lichfield', in 1767. His will was proved in the PCC 14 Sept 1812.
http://discovery.nationalarchives.gov.uk/SearchUI/Details?uri=D204718The Clergy Database provides a summary of his church appointments.
http://theclergydatabase.org.uk/Venn's
Alumni Cantabrigienses (available on Ancestry as 'Cambridge University Alumni, 1261-1900') has his parents as John JAUNCEY, gentleman of Middlesex, and Mary (HOLT), and provides further information on his career.
The RAWLINS will transcribed above refers to John JAUNCEY as both the testator's brother (part 1) and his brother-in-law (part 2), so perhaps it isn't a straightforward sibling relationship. It may involve a 'step' relationship (sometimes given as 'in law'), or perhaps there was an intervening marriage?
Two John JAUNCEY wills from Middlesex were proved in the PCC in the mid 1700s, either or both of which might help you.
John JAUNCEY, Gentleman of St George the Martyr, Middlesex, 1744
http://discovery.nationalarchives.gov.uk/SearchUI/Details?uri=D516550John JAUNCEY, Gentleman of Southampton Row, Middlesex 1768
http://discovery.nationalarchives.gov.uk/SearchUI/Details?uri=D502579That's always presuming I've read the surname correctly in the first place
