It appears the surname spelling is Baskiville, which then starts to bring up a wealth of information. Have a look online for births deaths and marriages:
https://bdmhistoricalrecords.dia.govt.nz. There are other Baskivilles listed.
Marriage: 1923/10409 Anita Doreen Underwood Walter John Baskiville
Death: 1979/41419 Baskiville Anita Doreen 9 March 1903
Death: 1976/42059 Baskiville Walter John 21 December 1893
Papers Past also provides interesting information:
http://paperspast.natlib.govt.nz/Evening Post, Volume LXXXIX, Issue 127, 31 May 1915, Page 2
‘CONVALESCENT. AUCKLAND BATTALION. 12/964 Pte. Walter John Baskerville (W. L. Baskerville. Police Station, Devonport, Auckland)’
Evening Post 16 December 1908 Page 8 BREAKING AND ENTERING.
Walter Joseph the father is a police sergeant stationed at Mt Cook and Walter John has a brother Henry Baskiville
Wills/Probaates at
http://www.archway.archives.govt.nz/Anita Doreen Baskiville widow Hamilton probate - possibly indicates they lived in the Waikato area.
Have you tried the telephone directory – there are only 3 Baskervilles listed for the whole of the country
http://yellow.co.nz/whitepages/searchHappy searching
Margaret