There were 11 James Watson's baptized in Scotland in 1777
There were 14 James Watson's baptized in Scotland in 1774
There will be several born who are not baptized therefore no records; and there will be many other records lost. And then, he could be from Northern England which opens up a larger can of worms.
A Sergeant Major was a full time profession they did not hold another job. The only time would be if he lost this position or if the Militia was disbanded and there was no other position in another Militia available.
The Fife Militia was not disbanded during this period, he couldn't "quit" and run off to Roxborough without obtaining a release. And...there was no such thing as the Kelso Militia. Kelso is in Roxborough.
James born in 1802 was the son of a Weaver not a Sergeant Major. Then in Feb 1803 a newborn child was buried a newborn child and an Anne died in April of the same year.
https://www.scotlandspeople.gov.ukIf you really want to know who Sergeant Major James Watson was you need to acquire his records with the Roxborough Militia. Since many records for the Militia are held (if they exist), locally I would suggest you contact
http://www.bordersfhs.org.ukDon