Okay, so... the next Eeveelution will be Dragon.
Let me explain my reasoning.
Aside from Fairy, all the Eeveelutions have fallen into categories that used to be classified as Special Attacks.
It is safe to say that Fairy would have been a Special Attack.
Looking at the chart, you have the following from the games that maintained the Attack Type determined by Move Type.
So I am calling it. Eevee will be Drakeon or some similar name.
This is the closest a Pokemon game has gone to launch without releasing a new Eeveelution, so Dragon is fitting as the final one.
Does anyone see a flaw in this logic?