How would I be able to stop the "Eye Bones" from interacting with the Body Mesh? The eyes are already their own mesh and the Eye Mesh is already parented to the Eye Bones. But when Parenting the Body Mesh and the Armature, somehow the Eye Bones took control of the face.
When you parent a mesh to an armature, the automatic weight function assign some weight to all bones marked as "deforming", no matter if they are controlling other meshes (a bone can control more than one mesh).
To solve the problem, select the body mesh, enter edit mode, select all vertices, in the properties window, vertex group tab, select the group named as the "eye bone" and click "Remove".