Hi Bob
Can see just two listings for an "Alexander CRAIB" on New Zealand electoral rolls - one in 1896; and the other from 1905-06 through to the 1940's appears to be the (1878) New Zealand-born Alexander.
1896 - Otago - Waitaki Roll
CRAIB - Alexander - Waihao Forks* - Schoolmaster[* Waihao Forks was a small community in the South Island of NZ, it's nearest largest town, Waimate, being some seven miles away. ]
Waimate (which seems a possible burial place for this Alexander) has an online cemetery database, but for some reason the website is not displaying the required information at present.
Maybe someone here with access to the burial locator might be able to check for the 1905 burial.
Otherwise could find no possible arrival date in NZ (though a passenger list entry may well have been mis-transcribed as say, "CRAIG" ?? ) ... and newspaper items yielded nothing either.
I'm guessing the 1871 Scotland census listing you have for your Alexander, perhaps doesn't show him with an occupation ?

~ Lu