Tasmanian Names Index
I've used this site often and found it very helpful.

John Jenkins' wife Matilda, nee Somers, died 3 March 1896 during childbirth, whilst giving birth to Albert Ernest. When Albert Ernest Jenkins joined up in 1916 he gave his sister Aleshia, (Mrs. H. Gittus) as next of kin. So, I narrowed it down to those 20 years between thinking the father may have died; but then maybe the son added the sister because she was literate and perhaps the father wasn't. all longshots but sometimes they pay off. Albert Ernest was living in Macquarie Plains when he joined up also his sister gave her address as Kentdale, Macquarie Plains. Then in his army records I found a letter asking for news from a Grace Wilson and in it she states she asked his parents for news; so then I think maybe his father remarried. Which is very probable.
The records I found were at the National Archives of Australia and the Tasmania Names Index.

another thing I meant to mention; Albert was wounded 3 times in battle the last time a bayonet in the foot.

[Wednesday 12 February 1919 published in 'World' Hobart Tas,]
Welcome Home Social.
A most successful welcome home social was tendered to
Sergeant Albert Jenkins, Privates Harold Gittus, R.Mason,
Arthur Brown, Clyde Lewis, and C. Reader, in the Upper Derwent United Hall
on February 5 (writes our Glenora correspondent). Eloquent addresses
were given by Mr. W. E. Shoobridge, M.H.A., and Messrs. V. W. and H. W. Shoobridge.
Sergeant Jenkins ably responded on behalf of the soldiers, giving a graphic
description of the Red Cross work on the battlefields of France.
The hall was very tastefully decorated for the occasion. After the ceremony
dancing was indulged in.

The Mercury (Hobart, Tas.) Thursday 19 Mar 1942
Page 6
JENKINS.—Funeral of the late Mr.
John Jenkins will move from his
daughter's residence (Mrs. H. Gittus),
Kentdale, Macquarie Plains, Thursday
(This Day), at 1.30 p.m., for Red Hills
Cemetery. Friends invited to attend.

Now you need a death certificate, might be some info on that

Here's the Death Notice, it gives his age

The Mercury (Hobart, Tas.) Wed 18 Mar 1942
Page 6
JENKINS.-Passed peacefully away on March 17, 1942, at the residence of
his daughter (Mrs. H. Gittus), Kentdale, Macquarie Plains, John Jenkins,
relict of the late Matilda Jenkins, aged 86 years.

that's the same address the daughter gave when she wrote to Base Records looking for her brother.