Errors vary from a few metres in the central regions of the map to a kilometre at the extremes.
The false northing value you just entered is wrong. On the Garmins, you can only enter 7 digits, not 8, so enter 9563802.0. But watch out when you enter waypoints directly into the GPS derived from a map. There is no accuracy lost by using the wrong False Northing value. The real errors come from using the UTM projection instead of the NZMG projection.