I'm slightly concerned that the Cecil A who came to Sydney has given "Farmer" as his occupation, when "other" Cecil was working on a farm in 1911.

Name: Cecil A CHRISTIAN
Date of departure: 3 December 1913
Port of departure: London
Passenger destination port: Sydney, Australia
Passenger destination: Sydney, Australia
Date of Birth: 1895 (calculated from age)
Age: 18
Sex: Male
Occupation: Farmer
Passenger recorded on: Page 9 of 12
Ship: WILCANNIA
Official Number: 110154
Master's name: P W Scott
Steamship Line: P. & O. Branch Service
Where bound: Australia
Square feet: 5152
Registered tonnage: 3129
Passengers on voyage: 236
Country of last permanent residence: England.

If this is the Cecil you are looking for, Australian records should make it clear who this Cecil's parents were. Do you have his death cert? Marriage cert? If not, these should be bought first, so that you don't go on a wild goose chase through IOM and UK records.
They can be bought online for NSW. www.bdm.nsw.gov.au/familyHistory/searchHistoricalRecords.htm
1929 Marriage? Is this the right one?
3211/1929 CHRISTIAN CECIL A [to] LUCKETT MILLICENT L [at] TAMWORTH

1959 Queensland Death?
Reg # Given Names Surname Father's Name Mother's Name
1959/C371 Cecil Arnold Christian Thomas Margarite Caine

I see your problem. Both parents different from expected? The accuracy for a death record depends on who supplied the information.

At least he would have given the info himself for his marriage - would you please post the details? He would not have known either of his parents if he was the Cecil whose parents died the year of his birth, but surely would have found out when he was older?

Sue