Well, Ann record of death has arrived, and it confirms a few deatils, and but no grave location. (Why is the quality of the scan sooooo bad? gah) I wrote back and asked if they could explain the fields on this register image... they noted that in 1861 the place of burial was not asked for. So the government does not hold that information, unfortunately.
Here is the record... the best I can make out...
Death Registration Record (Timaru District)
Source: New Zealand "Registration Act, 1858", Section X
Quarter Ending: 31st December 1860
Entry No.: 13
Date and Place of Death: November 16th, 1860, Timaru
Name and Surname: Ann Williams
Sex: Female
Age: 35
Rank or Profession: Publican's Wife
Cause of Death: Apoplexy
Signature, Description, and Residence of Informant: Richard Smith Cole (Barman, Timaru)
When Registered: November 18th, 1860
Signature of Registrar: B Woollcombe
(Apoplexy was a cerebral haemorrhage or stroke, and Belfield Woollcombe was the town's magistrate employed by the government.
Death Registration Record (Timaru District)
Source: New Zealand "Registration Act, 1858", Section X
Quarter Ending: 31st December 1860
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Entry No.: 13
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Date and Place of Death: November 16th, 1860, Timaru
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Name and Surname: Ann Williams
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Sex: Female
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Age: 35
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Rank or Profession: Publican's Wife
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Cause of Death: Epilepsy
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Signature, Description, and Residence of Informant: Rich'd Smith (Barman, Timaru)
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When Registered: November 18th, 1860
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Signature of Registrar: R.W. Tottenham
Side quest 1... Who was Lieutenant Belfield Woolcombe
He was the government's Resident Magistrate, her arrived in Timaru in 1857 and built a house at Ashbury Park.
In 1850s New Zealand, a government registrate/registrar, was responsible for maintaining public records, especially those involving births, deaths, marriages, and land transactions. He also wore a few extra hats, like Beachmaster and church warden.
I had assumed, as this was Woolcombe's job, that the records would be better, I'm not sure why. His records are not at the local museum, and are looked after by the government. You can search these online and see a basic level of information, but you have to pay and order a printout to be posted to you to see any details. - Which I have done for Ann and am eagerly waiting for... although I am realistic the paper work may not cite a burial plot.
Side Quest 2... who employed Woolcombe...
From 1928 to 1985, the seat was held by two Labour MPs: Rev Clyde Carr a Christian minister who was a supporter of John A. Lee and remained a backbencher; and then Sir Basil Arthur a hereditary baronet and later Speaker of the House.
https://en.wikipedia.org/.../Timaru_(New_Zealand_electorate)