Leaving Third House you should ride back the way you came for 20m then take a sharp right turn back onto the Dun Mountain trail. The trail is more undulating for the next 4km, with a few steep pinches to negotiate (easy on foot, tough to ride). After approximately 4km the scenery will change from native forest to a mineral/alpine environment.
Continue on past Windy Point (which is often very true to its name) and take the time to look behind you as the view is stunning. 2km further on and you'll be at the Coppermine Saddle, the high point of the ride (878m above sea level).
There is a toilet just past the saddle, off the track to your right.
From here it's all down-hill, so it's a great place to put a jacket on, take a drink and have some food.