I'm currently looking to edit an existing 3D model. I would like to select the eyes, but there are parts of the eyes with unexposed faces and vertices that are hard to select with the standard selection tools. Is there any way that I can place a sphere over the eye and just tell Blender "select all vertices in this 3D area"?
From your question I supposed is one object.
You can use the tool from Edit mode - Select - Select sharp edges: https://docs.blender.org/manual/en/latest/modeling/meshes/selecting/sharp_edges.html
... an old method is to select faces, edges, or vertices with these keys: Shift + Alt and click to select all connected.