Re: 1871 Curious Perfs 2d Vermillion 12.5 x 10???
The annotation on the back is 10 x 12½ which implies the top and bottom are 10 and the sides 12½ which would make it SG 130 (CP A2r) however the illustration looks as though it is 12½ x 10.
As you say SG only list an irregular compound perf, i.e., perf 10 on one vertical side only, SG 130b (CP A2r(X)).
CP list a variety under A2s (perf 12½) - 'mixed perf (re-perforated 10) and whilst mixed perfs usually show two rows of perfs on the relevant side of the stamp, of different gauge, if the stamp is separated along the inner row of perfs then you could end up with irregular compound perfs (where only one side has the different gauge) or compound perfs if two sides are affected. Some catalogues refer to these as mixed perfs, even if two rows of perf do not show on the one side, arguing that what you see is the result of re-perforating rather than the use of different perforating heads being used to produce the original perfs.
It is entirely possible that your stamp has been re-perforated 10 down both vertical sides and because of the way it has been separated from the sheet does not show evidence of an original row of perfs.
Viewed from the back the left side of the stamp shows evidence of a line watermark from the edge of the sheet. Stamps from the edge of the sheet sometimes end up with a wide margin. This sometimes justifies re-perforating by the government printer. However if left uncorrected it does provide the potential forger with room to practice his art!
I mention the latter only because forgery is a possibility here. To me the vertical perforations down the right side (left when viewed from the back), where any margin would have been, look very clean cut compared to those on the other vertical side. For this reason, and the fact that your stamp is potentially an unrecorded variety, I would suggest submitting the stamp to the Royal Philatelic Society of New Zealand for certification.
If you do - please post the results back here. I would certainly be interested in their opinion.