David,
Re: Jessie's Birth.
Jack's Lighthouse career record backs the 1878 departure to Japan. I have found a record in the Marine Births For 1879 listing a Female 'Burnet' ...... 1 't'. The scanned document is not clear on the internet but the name of the Ship began with 'A' and looks like 'Alhalbred' or some such name. I am going to dig out the document at the FRC in London as I live & work in London.
Re:James Burnett junior
I have James Burnett Junior's birth certificate. He was John James (Jack's) son and there is a trend of naming the first son after the Father's Father and the first daughter after the Mother's Mother. Hence Catherine Edith Burnett was named after James Burnett senior's wife Catherine Burnett (nee Sayle).
She being your Great Grandmother and my Great Great Grandmother.
Re: Swan Hotel
My dad went to Isle Of Man after his time with your Grandmother. I wonder if Gordon went with her to Australia yes? My dad recalls Robert Alexander Burnett was another of Jack's children and he went on to run the Swan Hotel. His son Henry Burnett suceeded him at the Hotel.
Re: James Burnett Senior
I think i have discovered the death certificate for James Burnett senior died 1889 aged 72 in Birkenhead, Liverpool. I have asked for a copy from GRO. This conflicts with your post saying he died 1885? I only have the census record of 1881 when he was on the IOM as you also discovered....This census return says he was born in Scotland. How did you get his death date and birth in IOM?
I will see my very ill dad on Thursday 25th with this detail and will mention all of this to him. I will let you know who and what he further recalls!!