There could be many interpretations if this is a fictional or fan - created story. Maybe 'kakyoin' is a character in a particular universe, like a game or a comic, and the idea of laying an egg is some sort of strange or magical event within that context. But without more information, it's hard to say for sure.
One common theme is friendship. They might explore how their relationship could develop in different ways compared to the original male - male dynamic in the series. Another theme could be adventure, with them going on new quests together.
There's no way to really tell if it's common specifically for someone named Jojo. However, in general, reading fanfiction is a popular activity among fans of many different franchises. The Jojo series has a large and dedicated fan base, so it's likely that there are fans named Jojo who partake in reading fanfiction, but we can't say for sure how common it is without more data.
One possible plot could be that Kakyoin and Jotaro come across a mysterious horse in their adventures. This horse has some special abilities related to the 'Stand' powers in 'JoJo's Bizarre Adventure'. They then have to figure out how to handle this horse and how it might be related to their mission.
Perhaps this Jojo is interested in exploring different interpretations and stories within the Jojo universe that fans have come up with. Fanfiction often takes the existing characters, settings, etc. from the original Jojo series and creates new and unique storylines. So, this Jojo might be a big fan of the series and wants to see what other fans have imagined.
There might not be a lot of fanfic specifically focused on 'kakyoin x jotaro horse'. It could be a rather niche concept. You may need to look through general fanfic collections about these characters and see if there are any that incorporate the horse element in an interesting way. For example, perhaps a story where they go horse - riding together in a particular setting within the 'JoJo's Bizarre Adventure' universe.