Two hours later, police collared him and charged him with doing an indecent act in public.
Initially the 54-year-old told officers there was a magnifying glass on the other side of the mirror which he was using to assist with reading but later pleaded guilty to the police charge.
In interviews with probation, Turoa acknowledged his behaviour was "wrong, creepy and sick" and said he did it because of stresses in his family life.
While probation called him a "real risk" to society and his young grandchildren, Judge John Bergseng said the offence was at the lower end of the scale.
"You don't know why you did it but experienced a great amount of shame for your family," he said.
"The victim was completely entitled to go about her business in a public place without being subjected to this behaviour from you."
The judge said the young victim would no longer visit the library for fear of it happening again.
A spokesman from the Waipareira Trust said Turoa had resigned from his position after being charged but the defendant hoped to find work again after undergoing counselling.
The court heard how the defendant was convicted of a similar offence in 1982, which involved alcohol and a friend's girlfriend.