- You may be looking for the Time Lord this construct is based on.
The Doctor shared the history and personality of his non-virtual counterpart, only parting with that history shortly after the events aboard Chasm Forge, meaning that he too was blind. He was a perfect duplicate and, like the rest of the people living within the Shadow World, he believed himself to be real.
He was in his lecture hall at St Luke's University when the Pope arrived. After some initial confusion caused by his partial blindness, even with the assistance of his Sonic sunglasses, Nardole helped him understand they desired for him to read the Veritas, a document that caused anyone who read it to kill themselves.
Travelling to Bill's house, he interrupted her date and brought her along, hiding the fact he was blind. One of the presets offered to give the Doctor confession through the Catholic Church after he had once refused Pope Benedict IX's offer as he felt it "[took] too long". Nardole cornered him before they left the TARDIS, confronting him over not telling Bill, but the Doctor brushed him off, being called an idiot on return. They were eventually taken to the Veritas, finding a priest had shot the lockout and read it. Although the Doctor understood the man was dead, he instructed Bill and Nardole to find him. Using the time alone, he borrowed regeneration energy from his future by using a device he attached to the temples of his head to briefly restore his eyesight to read it, though was confronted by the Monks, forcing him to flee with a laptop instead.
Despite nearly being captured, he made it to the Oval Office, finding the President dead, and (due to his eyesight fading again) listened to the Veritas via the laptop. He realised that he was part of a simulation created by aliens that wished to invade Earth. Bill arrived, whom he informed of such before she was deleted. Before being deleted himself, he used the sonic sunglasses to send an email to his real world counterpart to warn him of the impending invasion, musing that he was doing what everyone did when the world was in danger by calling the Doctor. (TV: Extremis)