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You may have quite a task, the fact that James was a member of the Presbyterian Church of Scotland, may suggest that there is a Scottish connection. The name Thompson is generally an English form of the name, in Scotland it is Thomson, then you have the way it is recorded, which is not always correct.
How do you know that James was born/baptised in Manchester?
This below might be a possibility, do the names of the parents appear in the family of James?
James Thompson
England, Lancashire Non-Conformist Church Records, 1647-1996
Baptism Lancashire, England, United Kingdom (This can include Presbyterian's)
Parents Richard Thompson, Hannah Thompson
They had several daughters but I can only see one son Richard 1801?
There are three others in Manchester on
https://www.familysearch.orgAll baptised in 1809, parents James Thompson, Rachel, Thos. Thompson, Jane Thompson, Thomas Thompson, Mary.
Plus this in 1808.
James Thomson Christening 5 August 1808
Manchester, Lancashire. Parents John Thomson, Ellen
Colin