It's definite that James was the son of the same couple. I have the record of his baptism by Rev. John Bethune of St. Andrews. It names both parents, identifies them as "of South Branch" and gives dob of 13 June 1799 and bap 30 June 1799.
This is actually my husband's ancestry, not my own.
Do you by any chance have Alexander's dates of birth and death? I've been told that he left a will, but not knowing when he died, I'm not sure how to look for it.