A year
It's something that is both considered a large length of time and a short length of time depending on who you ask and how you go about asking them. The answer will vary as the scenario you present can do so as well. However no matter the answer a year can be an extremely long amount of time. Anything can be seen as something unseemly long. It's all a matter of perspective that dictates the size of something no matter how what it is.
Breaking down a year it gets large and large the farther you go down the measurements of time.
12 months
52 weeks
365 days
8760 hours
525600 minutes
31,536,000 seconds
Of course, while the last one is the same as all the others before it and after it. No one really goes about truly experiencing time from the perspective of seconds. However, that is exactly how Toph has spent this last year of her life as she has been fully conscious and aware without moments of rest. There was no sleep, no zone out, nothing to distract her. She was always up and always knew exactly what was happening during every single second that passed.
Though for six months while her consciousness was in an endless state of awareness it was after this 'test' that was being conducted that she was truly one with the earth itself. This feeling of oneness that was all consuming during the first half of the years would have continued onward to the point where Toph would not even be aware that her consciousness had joined with the earth itself and become part of it. Part of the planet they were living on as the elements were not just that but they were alive in their own sense. They had consciousness all their own that differ from what even the spirits knew. Elemental spirits were not the actual element itself but merely an aspect of someone that failed to become a true bender but somehow form a new self as a spirit. Having a full aspect of that element but not truly being it.
Another thing Toph realized was that she could recall everything that has ever happened to her with vivid detail and some case better than she thought was even possible for anyone that human at least.
It seems this was also part of the test that she was being put through or at least this is what she thought as nothing was going to be answered for her as she knew the one that did this to her. They left her here to even succeed at their test or fail and then possibly suffer whatever result would come then.
Her own view of things was that one aspect of the test had to be that the person despite everything they were going through had to maintain their view of them being human the entire time. So with this in mind, Toph just went over her life as she had nothing us to do in this cavern and focused on her life as a human that kept fresh in her mind so that it would not drift away from her. Something that she felt firsthand and also nearly fall into herself as she was getting too caught up in yet managed to catch herself just being reaching that point of no return.
She had so far managed to cover everything up until the end of the Fire Nation's Hundred Year War. Although she had founded Beifong Metalbending Academy shortly after the war was over. That did not mean she got to work right away gathering students and everything immediately as well.
She knew a thing or two about how to run a business from overhearing her dad going on and on about his. He might have kept her hidden from the world until she was 12 years old. However, that did not mean he put his business on hold the entire time either. His work followed him home and she learned a lot of things from him during those times as enhanced hearing their overprotective nature made sure of that.
Thus before settling down create the Beifong Metalbending Academy. Toph was traveling around the Earth Kingdom visiting various places that she had been before with her friends as well as places she had never been before. However, the one place she avoided during her travels was her hometown of Gaoling. It was not as if she was avoiding her parents on purpose. She did miss them; it was just that she was worried that going back home would mean going back to the sheltered life that she lead there before meeting Aang and the others. She was not the helpless child that her parents thought she was and didn't she need to be placed on twenty four hour watch either. She was not sure what her parents thought of her role in ending the Hundred Year War and part of her did not want to know.
She was kind of proven right as her dad did not accept her right away and it took some time and well nearly dying. Only living through the ordeal because she was not a daughter her dad thought she was allowing him to see the error of his ways.
Made sense it would take something like that as seemingly being pushed into corners where they are forced to make a choice seems to be something that makes it clear they really are father and daughter.
Anyway, Toph was not just wandering around the Earth Kingdom for no reason at all other than to just travel and to avoid going home. The reason though for her travels was that she was trying to learn everything that she could about Earthbending. So far, she had mastered two forms of Earthbeding (traditional and sand) as well as created metalbending. This was not enough for her because she wanted to learn even more to become the first person that was an avatar to completely master their bending style.
