. Yes there was a second marriage for Edward John after the death of Eliza.These wills do tie in other family members
When I looked earlier at the Will of Edward John BUNTING ahead of the link being posted here, I thought there was something rather "odd" in respect of "his" children named in the Will.

The "daughter" Kathleen Mary BUNTING seems to have been born as "Kathleen Mary BIDDICK - 1911 reg. at Auckland" where her mother was residing. [Fair enough, she's probably taken on her stepfather's name. ]
There is a death though for the "son" Edward John BUNTING" - which shows he was (apparently) born 10 October
1918 
[Edward John BUNTING senior was still married to Eliza Emma in 1918 ?]
Edward John BUNTING (snr) - Will was dated 17 August
1926 and he'd married Laura B. BIDDICK a few weeks before on 26 July
1926. Eliza had died on
12 April 1926.
Seems a lot of action happening in several months in 1926.
Just simply curious about the dates .... and a "son" who shared his "father's" name being born in 1918 ?
~ Lu
PS : Meant to add that link below gives info on Joseph Hooper BIDDICK and Laura Brokenshire BIDDICK (nee HOOPER ) :
https://www.myheritage.com/names/joseph_biddick