I think the best way for you to find more information is to purchase the marriage certificate for James and Amelia.
I did find Amelia Sarah Gibson died 27 May 1920, and is buried in the Methodist Cemetery, Moorefields, NSW.
Good Luck!
Wende

I have done a little more research on this, and here is my opinion:
After Amelia died in 1920, James married Annie HOLMES (not sure if this is her maiden name or not). They lived at Peel St, Belmore according to the 1930 electoral roll. James is listed as a fitter, and Annie as home duties. James died in late April 1944, according to the funeral notices in the Sydney Morning Herald on 1 May 1944:
GIBSON. ?The Relatives and friends of Mrs Annie Gibson of Peel Street Belmore
are invited to attend the funeral of her dearly loved Husband James to leave our
Funeral Chapel This Day after short Service commencing at 3. 30 p m for Moorefield Cemtery, Dignified Funerals Lakemba UL2512
GIBSON.?The Relatives and Friends of Mr. and Mrs. W. Gibson. Mr. and Mrs. C. Gibson. Mr. and Mrs. A. McGaghey. Mr and Mrs. W. Barlow and Families and Mr.and Mrs. L. Staff are invited to attend the Funeral of their dearly loved father and Grandfather James. For further particulars see family notice Dignified Funerals UL2512.

Cheers
Wende

Australia Marriage Index, 1788-1950
Name: James Gibson
Spouse Name: Amelia S Gross
Marriage Date: 1890
Marriage Place: New South Wales
Registration Place: Sydney, New South Wales
Registration Year: 1890
Registration number: 1400

Australia Birth Index, 1788-1922 about Amelia S Gross
Name: Amelia S Gross
Birth Date: 1867
Father's Name: Charles Gross
Mother's Name: Louisa
Birth Place: New South Wales
Registration Year: 1867
Registration Place: Redfern, New South Wales
Registration number: 3810

Do you know if James had a middle name ?

I think this death is in the Lakemba/ Bankstown/Belmore area

Australia Death Index, 1787-1985
Name: James Andrew William Gibson
Death Date: 1944
Death Place: New South Wales
Father's Name: William
Mother's Name: Margaret
Registration Year: 1944
Registration Place: Bankstown, New South Wales
Registration number: 7518

Dear Noggin,Thankyou so much for your help.This information helps to confirm information that I have gathered from other sources.I am pretty sure thatJames Gibson was my paternal great grandfather.There is some mystery concerning his second wife who was said to have been able to speak German.My father often referred to her as his German grandmother.Holmes does not sound very German.Oh well,not a blood relative so not absolutely vital to my search for ancestors.Again many thanks for your help.Cheers,Keith Gibson

Thanks to Wende too.Lovely to see that others are interested and far more able than I.Cheers,Keith Gibson.

Hi Keith,
I am the Granddaughter of Janet Gertrude Gibson 1907-1977.
Her parents were David Dyer Gibson 1869-1942 and Adeline Alice (Ada) Batty (1876-1951).
I have Davids Birth certificate from 1869 and it says his Father was James Gibson, age 39 from Scotland and his mother is Mary Munro, age 35 from Scotland. They married in 1855
I come to a standstill as well at this stage of the tree.
Funny that you should mention the German ancestry as we always wondered why our Nan's middle name was "Gertrude". She was affectionately known as "Gert"
Could it be that maybe when Mary Munro from Scotland died, James Gibson remarried a German speaking lady?
Rachael Ellender (nee Liver)