Lawyers yesterday were finalising an accord between Speight and military head Commodore Frank Bainimarama in talks at the home of mediator and former Vice-President Ratu Josefa Iloilo.
Military spokesman Lieutenant Filipo Tarakinikini would not put a timetable on the negotiations, but remained confident a solution to the rebellion was close. "Very positive, very positive," he said.
Speight, claiming to be fighting for the paramountcy of indigenous Fijian rights, has refused to release Mahendra Chaudhry, Fiji's first ethnic Indian Prime Minister elected a year ago. But, now Speight has seen Mr Chaudhry's Government fall, the abrogation of the 1997 multi-racial constitution and the inclusion of his people on a committee to draw up a new constitution, he appears almost ready to end his siege.
"We're trying to do it this week," Speight said yesterday.
"This week we hope it will all be over. The chances are very good."
Half a kilometre away, at Cathedral Secondary School, an administrator, one of the school's few remaining staff, said students she had run into on the street were getting bored.
"They are eager to get back. The teachers haven't given them any work to do so we are just hoping they are doing some private study on their own," she said.
Across town at a petrol station, staff are run off their feet.
Attendant Anna Kitione said the station was one of the few businesses still trading since the coup.
"We close at 6 o'clock but the cars just keep coming and people beg us to reopen because they can't get their fuel or groceries from anywhere else."
Auckland taxi driver and ethnic Fijian Jioji Tikodei said he was sending money back to Fiji to support his relatives who had been laid off.
Fiji's tourism industry was losing an estimated $1.3 million a day and the hotel that employed Mr Tikodei's cousins had dismissed them a few weeks ago.
Now into its 34th day, the interest in the coup from New Zealand's Fijian and Indian community remains high.
Calls to Auckland's Hindi-language station, Radio Tarana, have been steady over the past five weeks.
Managing director Robert Khan said the station had seven correspondents in Fiji and calls were made daily to ordinary Fijians to see how they were coping.
Violence, particularly in rural areas, has been reported and he said there were continuing reports of businesses being looted.
George Speight talks to IRN's Barry Soper
(10 min).