I have reviewed info regarding Luke Gardiner. The 1851 census lists that he was born in Canada, not Ireland in about 1818. In 1851 Luke wife Mary and their three children lived in Mosa Twp, Ontario Canada.
This is the information I got from the history of Tehema County California:LUKE GARDINER, SR. was one of the old-time settlers of Red Bluff, having come to California in March 1854.He was born in Ireland[ think he was born in Canada] , August 13, 1818; was a farmer and a civil engineer.His father, Thomas Gardiner, a civil engineer and school-teacher, was born in Drumera, County Armagh, Ireland, August 12, 1767.
Does this info about Luke and Thomas seem like a match to your Thomas Gardiner?