So for some reason the resolution box in the options is blank and no drop-down menu exists for it. It's just a greyed out option. What can I do about this?
This occurs when the game is set to either Fullscreen (Windowed) or Windowed mode.
Fullscreen (Windowed) will default to your desktop's resolution setting. Windowed doesn't allow you to set a resolution as you can actively adjust the window size to change it.
If you set the game to dedicated Fullscreen mode, you can change the resolution in the section drop-down.
If you want the Windowed option to have a specific resolution, you can head to Documents\Elder Scrolls Online\Live and open the Usersettings.txt file. In there, you can edit these lines to your liking: