Fowlers modern English usage devotes a lot of space to discussing whether neither/ either is singular or plural and essentially there are plenty of examples of both forms being used. To me as a native English speaker both forms are acceptable so 1.Neither of us is a teacher. 2.Neither of us are students. are both fine. Just don't say "neither of us are a teacher" or "neither us is students".

In formal written English is a singular verb but still in spoken English it is ok to use plural