fallback to local authentication for non-admin/root users

This is not supported yet. Refer the article.

The BIG-IP system does not use local authentication as a backup method when remote authentication fails.

If your real need is to gain access for special non-admin/root users, you have to create those accounts locally on the box as exception. This would use local authentication than that of remote authentication specified.

tmsh create /auth user  role  shell  prompt-for-password