Often, the trainer will go on a search for Pikachu. They might explore different areas, ask other Pokemon or trainers if they have seen Pikachu. This search can lead to all kinds of adventures and encounters with new Pokemon.
Another way it could develop is that Pikachu might meet other groups of Pokemon. It could join them for a while and learn new things. Meanwhile, the trainer is desperately trying to find Pikachu and there are a lot of emotional moments as they both miss each other. The story might then build up to a reunion scene where they are both overjoyed to see each other again.
The story may develop with the village realizing she's missing and sending out search parties. Some characters might be sympathetic to her situation and try to help her secretly. Meanwhile, she has to deal with the physical and emotional challenges of pregnancy alone. After the baby is born, she may start training the baby in secret ninja skills while trying to keep their existence hidden from the world that might want to use or harm them.
He might first find a place to hide, like an abandoned building. There, he starts to realize how difficult it is to be on his own. He has to find food and water by himself.
Often, in addition to Eevee and Pikachu, their trainers might also be important characters. The trainers' actions and decisions can influence what Eevee and Pikachu do. For instance, if the trainer sends them on a mission, that becomes the basis of the adventure in the fanfiction. Also, sometimes other Pokémon that are friends with Eevee and Pikachu, like Charmander or Squirtle, might make appearances and play secondary roles in the story.
Maybe Pikachu is feeling neglected by its trainer. If the trainer has been paying more attention to other Pokemon or is too busy with something else, Pikachu might decide to run away to get some attention.
Their relationship could start out as a simple acquaintance. They meet by chance in a forest, for instance, and are initially cautious of each other. But as they face a common enemy, like a wild and aggressive Pokemon, they start to trust each other and become friends.
Their love story could develop gradually. At first, they might just be friends who help each other out. For instance, Glaceon could use its ice powers to create a path for Pikachu in a snowy area. As time goes on, they start to feel something more. Pikachu might start to get jealous when other Pokémon show interest in Glaceon. And Glaceon might feel sad when Pikachu has to leave for a while. This would be the start of their deeper emotional connection that leads to love.
I'm not sure of a specific title, but there might be some on fanfiction.net. You can search for 'Pokemon Ash runs away' in their search bar and look through the results. Some might have Ash running away to find a more peaceful life with his Pikachu, away from the chaos of the Pokemon League.
One possible fanfiction could be about Ash feeling overwhelmed by the constant battles and expectations in the Pokemon world, so he runs away to a secluded forest. There, he discovers a rare and mysterious Pokemon that changes his perspective on his journey.
Typically, the story starts with the Pokemon characters going about their normal day. Then, they happen to come across the mistletoe. There's an initial moment of shock or surprise when they realize what the mistletoe means. After that, there's a build - up of tension as they consider whether or not to kiss. Eventually, they do kiss, and then the story might explore how their relationship changes as a result.
In a far - off land, Pikachu fell in love with a Gardevoir. Pikachu was enchanted by Gardevoir's grace and psychic powers. Gardevoir was initially hesitant because they were so different. But Pikachu's persistent kindness won her over. He would sit and listen to her talk about the mysteries of the psychic realm. As they got closer, Pikachu's love gave Gardevoir the courage to embrace their relationship, and they became an unlikely but loving pair.