Tyson has never felt alone.

Given enough time a room full of monkeys with typewriters will make the complete works of Shakespeare

Tyson has never felt alone because of mathematics. He knows the laws of probability and that there are a finite combination of letters in the English language that make words.

Tyson knows that statistically there are going to be other people who have had the exact same thoughts as him, who likes the same things, who wants the same things. He'd always known this because of mathematics. 

Tyson has felt lonely and craved the company of other people but he had never felt alone, because he has never been alone, he isn't alone, and he will never be alone.

Broad Street and Lane

Tyson's home and pet shop are both on Broad, but not the same street. His Pet Shop is on (Old) Broad Street whereas his house is on Broad Lane. Tyson finds that symmetry comforting and has the money to waste on having that comfort.

Tyson lives where he lives because he has dogs and Broad Lane is in the perfect location to take the dogs to the parks, he is surrounded by them. In his main universe, Tyson was gifted this apartment by the Moriarty Mirrors as a gift. It was a former safe house of theirs and a place where Tyson would be comfortable and safe, somewhere to convince him to stay with them; that he was 'at home' with them. This apartment's close proximity to Heathrow also made it a valuable safe house and useful position to keep one of the Moriarty Mirrors' pets.

Tyson generally refers to the shop as being on Broad Street because - amongst a large number of people who live in or around that area in London - Old Broad Street is just called Broad Street, whereas New Broad Street was called New Broad Street. He chose the empty store lot on that street to make his store because of how convenient it is. It's only a few building away from his butcher, Jeremy. The shop is on the corner where Throgmorton Street joins it.

Tyson's buildings / territory

Tyson had many different places registered in his name as well as several areas that he thinks of as his but legally aren't.

The obvious ones are his London apartment, pet shop, and the family manor (registered to both him and Jethro). Army!verse has its own home.

Tyson also owns two storage facilities. On the other side of London to where he lives Tyson owns a storage locker where he keeps his motorbike and a few spare parts for the bike. Tyson doesn't keep anything else there because any other storage he requires, that he doesn't want to send to the family manor goes to the warehouse Tyson owns outside of London, near Bath.

So far Tyson has barely filled one-sixth of the warehouse but his intention isn't to fill it, it just to find homes for spare parts. There is a small work shop where Tyson will tinker with his devises / computers and tinker with his motorbike but other than that everything is pressed up against the wall or in boxes. There are the part if his old motorbike, which is does intend to do something with eventually, as well as several dismantlement computers. He keeps a lot of spare parts here as well as several books, mostly mathematical, and a handful of maps. He adores engineering because it is visible mathematics and had wanted to find a large space he could use to work in where he wouldn't get disturbed by anyone he didn't want to run into.

Scattered around the rooftops of London are Tyson's storage boxes. They are hidden from view and require Tyson's fingerprints to open but Tyson knows where all 64 of them are. He keeps different items in different boxes that vary from keys and money to fake IDs all the way to knives, guns, and ammo. These are his emergency supplies for quick escapes. Tyson had made sure that the boxes can't be found by mistake - hiding them in walls, under tiles, and above the line of sight - and that they will stand up to the trials of weather. He considers the sections of rooftops that his boxes are stored in as his - mentally and through the colour association of his Synesthesia - even though they aren't legally. 

Mathematical books

When Tyson wants to relax he'll re-read his mathematical (text)books. He had several, mostly kept under his bed, but his favourite are his tattered and dog-earred copies of:

1. Games of Life: Explorations in Ecology, Evolution, and Behaviour by Karl Sigmund
2. A course in pure mathematics by G. H. Hardy
3. The Principia: Mathematical Principles of Natural Philosophy by Sir Issac Newton

Morality

How moral is your character? Where would they be placed on a traditional alignment chart?

Tyson would be a lawful neutral, almost a true neutral but closer to evil than good.

Good - Neutral - Evil

Tyson has a moral code that he follows but because his job means blindly serving others regardless of his own views Tyson has bent the needle on his moral compass enough that he can use other people’s compasses. Tyson’s morals change depending on who he is around.

Example: When around Moriarty murder is fine, everything is fine, so long as he remains loyal to Jim despite that he has described Jim as follows, “Some men follow their moral compass like a golden thread. Others let it sway with every step. Jim, well, he uses his moral compass as a yo-yo.”

Tyson’s behaviour and views change depending on who he is around, so when he is alone and following his own he keeps to his own views which are mostly moral and correct.

When he is following his own compass he tries to be good - he does his best to help people and make people happy at the cost of his own happiness - so he could never be evil but, even [especially] to his own mind, he has done far too much bad to ever be good.

Lawful - Neutral - Chaotic

Tyson has far too many [nervous/OCD/general] ticks and routines, is far too predictable, to be chaotic or neutral. He has created too much structure in his life to be anything but lawful. Even the way he chooses when to be good or bad is lawful, it is dictated by those he is around rather than chance or his own opinions.

But he is mentally unstable enough to almost be a neutral. He is just after the boarder. Over time as he becomes more and more derailed he may drift over to being a neutral, though it is highly unlikely that he could ever loose enough of his ticks and routines to go over to chaotic.