Well, it can be a bit difficult to find good ones right away. You may need to dig through different fanfic communities. Some smaller, niche fanfic platforms might also have such works. But keep in mind that yaoi fanfics often explore different interpretations of the characters' relationships, so you might have to read a few to find the ones that really suit your taste.
A really interesting plot point could be the clash of cultures. Harry comes from a world of magic and mystery, while Booth is used to a world of forensics and modern law enforcement. So when they meet, their different ways of approaching problems and their distinct knowledge bases create a lot of drama and intrigue.
There are often fanfictions that explore the idea of Harry Potter and Seeley Booth teaming up. For instance, in a story, they might be brought together by a common enemy. Booth's skills as an FBI agent and Harry's magical abilities would make for a great combination to fight against dark forces that are threatening both the wizarding world and the normal world that Booth inhabits. It could involve a lot of suspense and unique plot twists.
In some yaoi fanfics, their relationship might be one of mutual understanding and hidden passion. They could be portrayed as having a deep emotional connection that they struggle to express in the context of their work or the world around them.
I think you'd have to look up his birthdate and calculate based on the release year of the movie. Maybe do a quick search online and you'll get the answer.