Hi there,
Long post

I am not as familiar with NZ searchings, as say with NSW searchings.
I have a fair understanding of the admin side of the NSW marriage registrations in the 19thC (Church and Civil aspects). NZ admin was hived off from NSW admin 1840, and its BDM admin system may have similiarities with NSW.
If so, then until the civil regulations sorted themselves out from around say 1875ish, the civil registration is not as detailed as it could be. One issue in NSW was about who could handle the civil registrations of marriages, as there is often SCANT info on the actual Civil registration held by BDM register. (for example a huge debate over if a clerk was permitted to read, register, etc the details about a marriage IF that clerk was not of that denomination .... part of that debate that raged for DECADES in NSW 1850s to 1890s).
I particularly mention these things, because, in my view, where the clergy have completed the signatures sections, it is likely that that particular record is simply a SUMMARY of the actual parish register that the clergy retained in their safe keeping, and the clergy forwarded only the brief details.
Long before fh was as popular as it currently is, (so long before the internet), I was hunting out original registers to follow up on family history research conducted in the 1930s by one of my grandparents who HAD located original registers and had therefore found the FULL details about the parents and the bride and groom that had been given to the clergyman when attending the interviews PRIOR to the marriage. (In NSW it seems it was all denominations who recorded the full details, but simply did not provide all the info to the civil registers). I had the "bride's copy" of the clergy issued mc, I had the NSW BDM issued mc, and I had my grandparent's transcription of the actual parish register. Only on the parish register was I able to find the names of the parents of the bride and groom. Sometimes I needed to find FIVE different registers to obtain ALL the info given to the clergyman.

(One of which is akin to the ITM records archived in NZ)
I am very familiar with how to find the elusive details about the parents of the bride and the groom where the marriage was celebrated in NSW in those years. Simply put, you get to the Church register. (Often now these are in safe custody of the various denominations 'head offices', back in the 1960s and 1970s they were up the back shelves of cupboards in Manses, or as door stops or footrests etc).
I see no reason for the NZ Presbyterian registers to have LESS info on them that say on the NSW Presbyterian registers in that same time. There are some exceptions, as unfortunately for fh buffs, there were several "marriage shops" in Sydney at one time, and those clergy were quite scant in the details they noted.
In the 1870s, NSW Presbyterian registers for marriages include

the bride's parents names (including Mum's maiden name and any former names) and Dad's occupation at that time; the bride's age, place of birth, occupation, usual address.

the groom's parents names (including Mum's maiden name, and any former names) Dad's occupation at that time; the groom's age, place of birth, occupation, usual address.

if EITHER bride or groom is not yet 21 years of age, then the name of the person, and their relationship to the bride or the groom, thereby giving consent to the marriage.
Cheers, JM