I found what could be Charles Gilchrist's baptism. It is possible that Charles was born in 1770. There is a baptism record of a Charles Watson Gilchrist, born on 29 January 1770, in New Saughton (Edinburgh) baptised 4 inst (February) 1770. His father was John a gardener and his mother was a Betty Struthers. The name of Struthers appears as a family name in later generations of Charles Gilchrists ancestors which might suggest that the baptism is correct. His age was given as 59 on the records of his death in 1829 which ties in with a birth in 1770.
Payroll records of the Fifeshire Cavalry at the National Archives, show that Charles joined the Cavalry in 1795 and on the records for the second half of 1795, he is listed as "attested Sept 9". He served as a private until 1800. Charles arrived in Boston, Linconshire in the spring of 1798. In the summer of 1798 the troop had moved to King's Lynn, before returning to Boston, where Charles married in September of the same year. It doesn't seem as if he had known his wife very long does it. After his marriage, he was stationed at various places on the east and south-east coasts of England but his wife appeared to have accompanied him to some of the places as the payroll records show that he received a billeting allowance. The troop was eventually disbanded in 1800.
From the place he was baptised (and I don't know Scotland at all), I assume this is the same area as your ancestors were employed as gardeners but whether Charles' father was employed there, I don't know. If you have any info about Charles Gilchrist or his possible father John, or can advise me where to look, I'd be very pleased to receive it.
From what I've read, Provisional Cavalry Regiments were raised under an Act of 11 November 1796, - although the Fifeshire Cavalary was actually raised on 29 May 1794, - to be embodied in case of emergency, for service in Great Britain only. On 13 August 1799, they were converted to Fencible Cavalry. In March 1800, they were ordered disbanded. I thought they were under the command of Commander Major Cmdt. John Anstruther Thompson, although you suggest it was someone called Erskine.
Lizzie