The operation on Tuesday moved quickly, raising hopes that all 12 boys and their adult coach from the Wild Boars soccer team would be at the surface by the end of the day.
Monday's rescue mission, which saw four boys extracted before dusk and whisked to Chiang Rai hospital, took around nine hours.
The eight boys already evacuated from the cave over the weekend are being held in isolation - and aren't even allowed to hug their parents - as doctors assess them for histoplasmosis and other conditions.
Harris' colleagues and fellow rescuers lauded his commitment to the mission and how vital his expertise was in bringing the boys out to safety.
The boys and their 25-year-old coach have been trapped for more than two weeks after heavy rains flooded the kilometers-long cave network made up of caverns connected by tight passages.
"Everyone is in a good mental state", Jesada Chokedamrongsuk, permanent secretary of the public health ministry, told reporters at Chiang Rai hospital.
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The submarine has been dubbed "Wild Boar, ' named after the young boys" soccer team. "We will check later today whether their eyes have adjusted to light", said Dr Jesada.
Each of the rescued boys has been guided through the dark winding cave by a pair of divers.
According to Jonathan Head, BBC's Southeast Asia Correspondent, divers will go back for the remaining four boys and their coach on Tuesday.
His Highness Sheikh Mohamed bin Zayed Al Nahyan, Crown Prince of Abu Dhabi and Deputy Supreme Commander of the UAE Armed Forces said that he was glad to hear that the rescue operations were successful.
Their families were being kept at a distance because of fears of infection and the emaciated-looking boys were eating a rice-based porridge because they were still too weak to take regular food, authorities said.
"Doctors have treated the boys and now all of them are okay and cheerful".
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Two of the boys possibly have a lung infection but all eight are generally "healthy and smiling", he said.
Fresh rains on Tuesday added urgency to the final stages of the treacherous rescue bid, several kilometres inside a mountain and through flooded, tight corridors.
People across Thailand cheered the rescue operation, including at the Mae Sai Prasitsart school where six of the trapped boys are students.
But he added rescuers may need more than 20 hours, to replan and replenish oxygen supplies, to be ready to mount the next mission. "Hopefully useful. If not, perhaps it will be in a future situation".
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