When I reviewed my answer above, I realized that the rule applies to "two singular subjects", however, in your question the subject was not connected by "or, either/or, or neither/nor". So, I did a little more research by consulting the book called "Practical English Usage." The following is an excerpt from the book:
Determiners
When "none, neither, either and any" are followed by "of + plural noun/ pronoun", they are normally used with singular verbs in a formal style in British English.
Plural verbs are common in informal British usage and generally in American English.
- None of the cures really works. (formal British)
- None of the cures really work. (informal British; American)
- Neither of my brothers has/have been outside England.
- Has/Have either of them been seen recently?
- If any of the children gets/get hungry, they can have an orange.
So,
Neither of them IS (Formal British English)
Neither of them ARE (Informal British and American English)