Faces not recognized when photos are stored on external hard drive

Why not run a Managed library on your external drive rather than a referenced library on your internal drive

LN

When I configure iPhoto to not copy the photo from my external hard drive when it imports the photos, Faces doesn't recognize any faces.

that is a referenced library

But when I configure iPhoto to copy the photos from my external hard drive into its library, then it does recognize faces.

that is a managed library

in either case the library can be anyplace - on an internal drive or on an external drive

the referenced library has many disadvantages including making importing more complicated, deleting photo much more difficult and moving to a new computer or hard drive potentially very difficult

The issues with faces for you as best I can tell is the fact that you are running a referenced library - it had nothing to do with the location of the library

LN

Was the external hard drive with the photos on it mounted when you launched iPhoto for the first time and went through the upgrade? This is when face recognition happens and iPhoto needs to have access to the images. Also, after face recognition happens, you will not see any faces displayed in the faces area. You need to start by selecting a photo with a face on it and then click on the Name icon.
If your HD was not on and mounted when iPhoto ran the face detection, you can force the face detection to run again by deleting the face.db and face_blob.db files. Quit iPhoto, select the iPhoto library pkg, control click and select "Show package contents" remove the 2 files (do not move or touch anything else). Close the folder and launch iPhoto. Face detection should start again. If you click on the Faces item you will see a progress bar and the faces from your library being recognized. Wait until it's done before you start naming your photos.