This suggests an altogether earlier date for the birth of his son, Charles William Wilkinson, who was born in Edinburgh, Scotland when his father was serving in the British Army. The January 1880 obituary for Charles suggests he was 66 years, 6 months old when he died. In 1810, when his son Aaron was born and baptized in Sunderland, Durham, Moses' occupation was shown as "weaver". This fact suggests that Moses Wilkinson left the East Yorkshire Militia before Aaron's birth.
66 years and 6 months old in January 1880 still suggests a birth in 1813.
Can you assume that Moses occupation being given as weaver in 1810 means that he was no longer in the East Yorkshire Militia?
Not sure!
Why was he in Sunderland, and then in Scotland?
There are many references to the EYM in the newspapers, a few of them
Stamford Mercury, 10 April 1807
Tomorrow the East York militia, now on their route from Woodbridge, will march into Norman Cross barracks.
Ipswich Journal, 11 April 1807
Ipswich
Monday and Tuesday last, the 1st East York Militia marched into this town, from Woodbridge Barracks, on their route to Stilton.
York Herald, 25 August 1810
On the 4th inst. the Lord Bishop of Durham confirmed 860 persons in the parish church of Bishop-Wearmouth, among whom were about 50 soldiers, belonging principally to the East York Militia.
The Globe, 28 February 1811
Last week the East York militia arrived in Newcastle, from Sunderland, on their route to Scotland.
Stamford Mercury, 8 March 1811
The East York Militia have marched from Sunderland on a route for Scotland.
If you can pin down a death and burial for Moses you will have an approximate year of birth.