In most cases, neither means "not either." When used as an adjective either means "one or the other of two people or things," and neither means "not one or the other of two people or things." In other words, neither means "not either." The following example sentences show this use.

Which is correct neither has or neither have?

The strictly correct usage is "Neither...has..." (singular), but the "psychological" grammar is plural: "Both remain missing" is another way of expressing the idea, and as often (infuriatingly for non-native speakers) the formal grammar has been submerged in idiom.

Where do we use either and neither?

Alone: either means “one of the two”; neither means “none of the two.” Use a singular verb. Either combines with or; neither combines with nor.