This is probably pure coincidence but I just had to reply.
I am trying to kickstart my family tree research which has hit a dead end in Ireland.
My great-great-great grandfather Patrick Gately was born in Roscommon in 1796 and transported to Australia in 1821 where he married Mary Clogher (or Cloghen) in 1837. Their son John was born in July 3, 1846 - the same day Patrick received his full pardon.
Obviously they are not the same Patrick but the coincidence that compelled me to post was the fact that your ancestor Thomas shares my birthday and was born almost exactly 100 years before me.
Of course I am also hoping that these details my trigger replies in my own case. It's possible some of my Patrick's siblings emigrated to the US. IF anyone can make the link that would be fantastic.