I have been following the family tree of Eliza Sylvester, daughter of convict John Silvester and Martha Walton in Hobart, Tasmania. Eliza Silvester (Sylvester) was born 23 Feb 1848 Hobart, Tasmania and married John White in Hobart on 20 Nov 1867 (per Australian Marriage Index). They moved to San Francisco where their 3 sons were born, Allman, Charles and John. Eliza died abt 1918 or before 1920 and John White moved to Oakland, lived alone in 1920 and died not too long after.
I am not sure where the information of Eliza Mitchell came from but from my research, she is not connected to John White of San Francisco - not sure where John White was born - census records vary from New Zealand, Australia to Scotland - his parents were born in Scotland and John and his father both may have been mariners - John worked with shipping manufacturers.