"i know John spent time at Pekina,"
Which John is this....father or son?
Using Trove I see FITZPATRICKs and Pekina.
How/when do you place your FITZPATRICKs at Pekina.
"John A. c1854-27 Oct 1915 Adelaide"
Where do you see John FITZPATRICK, died 1915, with a second given name?. What is the second given name?
Are you descended from this FITZPATRICK family?
"Patrick born ?"
You had reason to believe there was a Patrick FITZPATRICK but did not have him to be on the "Tarquin" with his family.
Apart from the reasonable suspicion that a FITZPATRICK family from Ireland might include a Patrick, where have you seen something specific for your family?
The Advertiser 28 Oct 1915 p2
https://trove.nla.gov.au/newspaper/article/5485179?COFFEY.-The friends of Mrs. P. COFFEY, of Exeter, are respectfully informed - that
the Funeral of her late brother (John FITZPATRICK), of Solomontown, Port Pirie, will leave
47, Wakefield-street, on THURSDAY, at 11 a.m., for the Catholic Cemetery, West-terrace.