But one place where they are relatively easy to find is the island sanctuary of Tiritiri Matangi, in the Hauraki Gulf, where kokako were reintroduced in 1997 and now number 23 adults and at least three chicks.
I have written previously about the magical experience of a daytrip to Tiri but this time I was staying for three nights, including a couple of days when the 360 Discovery ferry from Auckland and Gulf Harbour wasn't running, so we had the island almost to ourselves.
Better still, sleeping in the island's bunkhouse it was remarkably easy to rise at 5am and race out to enjoy the incredible dawn chorus, with the deep ringing notes of the bellbirds, the musical gurglings of the tuis and, if you're lucky, the sweetly mournful serenade of the kokako.
It was on one such early morning excursion that I encountered the kokako on the Ridge Track, first feeding on the weeds, then running up a whiteywood tree to tuck into the profusion of ripe berries.
Fortunately I was accompanied by two of the island's volunteer kokako monitors, Sheryl and Neill Sutherland, who were able to identify the bird from its coloured bands as Te Hari, partner of Phantom, who was known to be raising a chick in a nest nearby.
Later, because we had official clearance from the Department of Conservation, we were even able to leave the track and watch the nest, timing the departures and arrivals of the parents to get an idea of the chick's age.
A couple of times we saw Phantom emerge from the nest and once even the shape of the chick. Meanwhile Te Hari dropped in with a takeaway snack, re-appeared 12 minutes later, then again 14 minutes after that.
"Typical male feeding pattern," said Sheryl, who has been doing kokako monitoring for several years, and after consulting the guidelines she said the chick was probably 4-5 days old.
Teams of volunteer monitors like the Sutherlands keep an eye on the island's kokako from around late September to early April, partly to ensure all is well, but also to feed information to the national kokako recovery programme.
Why, I wondered, did it matter exactly how old the chicks were? Well, said Neill, there was one example right before us. "It was planned to take Phantom and Te Hari's egg and give it to an infertile pair of kokako further south. But just before they were due to collect the egg it hatched."
I know such mixing is necessary to ensure genetic diversity but I couldn't help a surge of pleasure that Te Hari and Phantom had been able to raise their own chick - which they were obviously doing very well - rather than wasting their efforts on an artificial egg.
Meanwhile we were off to monitor another nest, this time one belonging to the island's senior pair, Cloudsley Shovell and Te Koha Waiata, who hang out near the Wattle Track. Cloudsley was named after a British admiral but turned out to be a female, a slip which I fondly imagine would cause the old mariner's wattles to turn blue with apoplexy should it ever come to his attention in the afterlife.
As befits two old hands, these kokako were extremely co-operative. TKW, as the male is familiarly known, was feeding on a clump of kawakawa bushes beside the track as we arrived. Then Cloudsley suddenly appeared on a branch almost above my head.
Possibly concerned at our presence, TKW gave a brief burst of song - "Calling her back to the nest," whispered Neill - and Cloudsley promptly glided back home. The pair would have felt confident leaving their chick alone, Sheryl added, because it was quite advanced. The chick then confirmed this by appearing on the top of the nest.
Over the rest of my stay I had many more kokako sightings: often feeding on the grassy tracks - on one occasion bouncing at least 10cm in the air as it bounded down the track - sometimes running up and down the trees, now and again perched high in the tree tops, in one memorable case feeding on the crimson flowers of a pohutukawa.
On the lovely Kawerau Track, which runs through a patch of ancient forest, we twice sat on the seats of the boardwalk and listened as a kokako sang a gloriously sad melody high above. It was probably Chatters, whose partner Te Rei has not been seen for some time, and could be either nesting or dead.
Such was the sadness of his song I had to think the news was bad... but then kokako always sound like that.
Of course we didn't only see kokako during our island stay. Saddleback alarm calls constantly sounded from trackside bushes. When we entered the bush we were often joined by robins hoping our big feet might stir up the forest floor and expose tasty insects.
While sitting listening to Chatters sing in the Kawerau Forest I twice looked up to find a tiny rifleman - our smallest bird - sitting nearby. And once there were three of them - should that be riflemen, riflemans or riflepersons? - perched on a sapling less than a metre away.
Small flocks of brilliantly green and red kakariki kept flashing by cackling like children bent on mischief. Families of whiteheads jumped excitedly from tree to tree. Fernbirds, which I've always thought shy and quiet, were all over the place and making a lot of noise. Down at the ponds the pateke, or native teal, were so friendly they waddled up to meet us.
Pairs of the notoriously unfaithful hihi, the males resplendent in their yellow, black and white plumage, the females a more subdued brown, kept up a constant barrage of clicks from the bushes. We got a closer look at them when the island's hihi researcher, Michelle Goh, invited us to watch her banding some of this season's chicks.
On the grasslands the common pukeko and the very uncommon takahe kept protective eyes on their new chicks as they nibbled grass. Poor old Greg - at 19 the island's oldest takahe, whose longtime partner Cheesecake has abandoned him for a younger bird - was making do with the companionship of a young pukeko.
We didn't see any tuatara but as a bonus I did get a glimpse of one of the newly released giant wetas .
DoC scientist Chris Green escorted us into the patch of bush where 10 days before he had put wetapunga - once found through the region but now surviving only on Little Barrier island - into temporary bamboo homes carefully positioned to offer good access to both food and places to hide. Three were still using this prefabricated accommodation but the others had headed out into their new world.
I've always been fascinated by wetas - I've even got a weta T-shirt - so it was a real thrill to see a female wetapunga, which will one day grow to weigh more than a song thrush, staring warningly from the top of her bamboo cave.
Visitors to Tiri are unlikely to see these new inhabitants any time soon but, with further liberations planned over the next few years, the population should grow and, who knows, one day people staying overnight might find their sleep disturbed by the heavy tread of the world's second largest insect.
But if that prospect seems a little scary, never fear: you can always rely on the feathered Lone Ranger for support.
Kokako Week
Tiritiri Matangi is celebrating the kokako with a special event from March 6-11.
The focal point of the festivities will be an exhibition featuring work based on the kokako by artists Bob Steiner (ceramics), Jane from Moth Design (bags, T-shirts, purses), Ingrid Anderson (tea towels), Reuben Price, Simon Fordham and Geoff Beals (photography), Tracy Huffman (jewellery), Sandra Whyte (paintings and prints) and Peiter Huisman (film).
There will also be a concert, which the kokako may decide to join in, on the evening of March 10.
Funds raised from the week will go towards the Tiritiri Matangi Kokako Programme.
CHECKLIST
Getting there: Take the 360 Discovery ferry service to Tiritiri Matangi.
Where to stay: For information about staying in the bunkhouse see doc.govt.nz/tiritiribunkhouse.
Further information: You can find out more about the island, and the planned Kokako Week, at tiritirimatangi.org.nz or watch a teaser clip on YouTube.
Jim Eagles stayed on Tiritiri Matangi with help from 360 Discovery Cruises and the Department of Conservation.
