Welcome to the Forum! The safest choice if you are writing a paper is to treat "neither of X" or "none of X" as singular (is, does). In ordinary everyday conversation, where people are more relaxed and more flexible in their use of language, both are used, and neither will stand out as particularly strange or out of place.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.