Hello Tom,
Yes i have done a bit of research on this family.
John Wylie, married Helen Beggart, 16/06/1804, Stevenston, Ayr.
They did not have a son Thomas.
John Wylie's, parents were Matthew Wylie, married to Elizabeth Baird, on 29/July/1769.
This couple had also seven children all born Stevenston, Ayr, again there was no Thomas.
Wylie/Wyllie, is a popular name in Ayrshire, in 1851 there were 976 people of those names.
Regards,
Jonn.