My cousin, who is the daughter of Ivy Esther Wilson -- the daughter of Sidney Wilson and Ethel May Clark, tells me:
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I connected Sidney to Thomas Wilson Garlick through my DNA match to Diane Garlick who turned up as an extended family match of 135cM, half 2nd cousin. I contacted Diane and we were both mystified as to how we were connected.
I started looking into Thomas Wilson Garlick, Dianes 2 x G Grandfather, he lived in Wollongong/ Clifton at the time & place where Sidney says that he was born. Thomass marriage had broken down by the mid 1870s, according to court information from Trove. From what we can gather Thomas was a bit of a rogue and have obtained a lot of information on him, and I believe Sidney was similar to Thomas.
After Sidney served in WWI he left the family, and not much is known of him. We think we have his correct death certificate.
After I put Thomas Wilson Garlick in my (Ancestry) tree, I have DNA matched with his family in particular through his maternal line. I dont seem to have any connection to Thomass wife, Mary Collaery.
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So as David Nicoll suggested, DNA is the key to establishing who was the father of Sidney Wilson -- Thomas Wilson Garlick. We just need to find the mother (who Sidney said was Louisa), and a birth registration for Sidney. So I will keep at it.
Geoff