OK I had time to look at this. What we have is a mismatch of face normals. Here is one way of diagnosing. First your metarig is messed up so I deleted it, added a new one. Deleted all bone vertex groups, which are all vertex groups. Delete armature modifier. Very poorly I scaled your mesh to match the new metarig. Into edit and position metarig very roughly. Generate rig. Yep I have the error. So. what part of mesh is causing this error? Well I just chopped off your head because if you look at your face normals they are going everywhere. Rigify does not like that. Moved it to another layer and extended the neck up to see if that was it. Deleted vertex groups, deleted armature modifier, and guess what. Yep it worked. Head must be the problem.
To fix it I secured another copy of your file. Put the metarig in as before since yours is messed up. Delete all metarig parts but the head and neck in edit mode just to make things easy to figure out. Now to work on the head. I selected the eye globe part inside your head (main mesh not the eyes) and your mouth and made those a separate part. Now I generated the rig and parented it to the mesh. It works. So your eyes and mouth on the inside have confused rigify. Fix your eyes and mouth and it will work.
Here are the test files.
You might be able to do the same and then flip those normals, ( I didn’t try it since I ran out of beer and now need to go to the store), but I think on the mouth your better off with a second part. The eyes I don’t think you really need that part.