There’s this one in 1885
Rimutaka, arriving Wellington July from London via Auckland, but seems odd they would be getting off there if he went gum digging.
But possible. Timing is good for marriage mid May
https://paperspast.natlib.govt.nz/newspapers/NZMAIL18850717.2.34?end_date=18-02-1886&items_per_page=10&page=3&query=franks+passengers&snippet=true&start_date=01-05-1885
*modified to add year
Hi Mckha
Have to say, I think your choice of voyage, above, is the most likely.

Problem is, apart from lists printed in various newspapers, there appears to be no "official" passenger list for this sailing of the "Rimutaka". (She had been in NZ earlier in 1885 also ... and there is a passenger list for that voyage.) "Rimutaka" (July arrival, 1885) does not show up in Archives NZ's listings (which sort of tells me, there isn't one).

I checked "Petone Settlers database" at Wellington - they have Mr and Mrs FRANKS arriving 1885 {"Rimutaka") BUT ... source of that information is the "Evening Post" - 13 July 1885 newspaper report. [Wellington City Library possibly has additional lists or info ... but heritage stuff is all packed away out of reach due to earthquake damage to now vacated library building.]
Two passenger lists published 9 July 1885 - "Auckland Star" ... and "NZ Herald" (the more comprehensive of the two). Neither mention, FRANKS though ?
When I checked these articles further, I noticed the "Second class" passengers were missing - (the FRANKS were apparently in that, group.)
A bit more digging turned up this >>
https://paperspast.natlib.govt.nz/newspapers/TAN18850704.2.12Shipping and Passenger Notes :
.... the "Rimutaka" passenger list is a wretched one ... And there at the bottom is listed "Mrs FRANKS"

~ Lu