One common plot is their exploration of different Alternian cultures together. Since they come from different backgrounds on Alternia, fanfictions might delve into how they share and learn from each other's cultural experiences.
Archive of Our Own (AO3) is a great place to start. It has a large collection of Homestuck fanfictions, including many about Eridan and Aradia. You can use the search function to specifically look for their pairing and then sort by kudos or bookmarks to find the more popular ones.
One common theme is the exploration of their different personalities coming together. Eridan is often seen as more brooding and Gamzee as more chaotic, so their interactions can be an interesting study.
Some fanfiction communities on Tumblr might also have 'eridan x gamzee fanfiction'. You can search through relevant tags or ask in the Homestuck - related fan groups. However, the quality can vary greatly, so you may need to sift through a bit to find the really good ones.
Another theme could be redemption arcs. Maybe Eridan has done something wrong in the story's context and Karkat helps him to become a better person. It can be a really interesting way to develop their relationship within the fanfiction.
One popular theme is their complex relationship. Given their different personalities and roles in the Homestuck universe, many fanfictions explore how they interact, argue, and sometimes reconcile. For example, some stories might focus on how Eridan's more abrasive nature clashes with Feferi's more diplomatic and kind - hearted side.
The fanfics usually have a lot of dialogue that is very characteristic of the two. Sollux's tech - speak and Eridan's more dramatic language can be used to great effect to show their individualities and how they interact with each other. It also often delves into their backstories and how those shape their relationship in the present.
A prevalent theme is the idea of redemption. Sometimes Sollux or Aradia might have something they need to make up for, and their relationship helps in that journey. Also, the theme of adventure is quite common. They might go on quests together, exploring new areas in the Homestuck universe, which tests and strengthens their bond.
You can try Archive of Our Own (AO3). It has a large collection of Homestuck fanfictions, including those about Eridan and Karkat. Just search for 'Eridan x Karkat' in the search bar and you'll get a bunch of results.
Don't forget about the pacing of the story. If it's a short fanfiction, keep the plot simple and focused. But if it's a longer one, you can build up the relationship gradually, with some ups and downs. For example, there could be a misunderstanding between Eridan and the reader that they have to resolve. And always proofread your work to make sure there are no grammar or spelling mistakes. You can also ask for feedback from other Homestuck fans to improve your fanfiction.