In this case the correct verb would be "have." This site may be helpful... http://owl.english.purdue.edu/owl/resource/599/01/

Either on its own is used with a singular verb: Wear red or white – either is acceptable. When it is followed by of, it commonly has a plural verb: Have either of you seen my glasses?, although in formal writing a singular verb is preferable: Has either of you seen my glasses?. When it is followed by or, the verb agrees with the noun or pronoun that comes after the or. If this is singular, the verb is singular: Either John or Kathie has got it. But if it is plural, the verb is plural: Either Frankie or his brothers have promised to be there. The second noun or pronoun also determines the person of the verb: Either you or I am right, but Either I or you are right. If one noun or pronoun refers to a male person and the other to a female person, it is permissible to use a plural verb and plural pronouns, in order to avoid the invidious 'he': If either Peter or Jennie ring, tell them I'll call them back. When you use either ... or, it is preferable to put both the either and the or immediately in front of the parts of the sentence they refer to. So: You must either pay up or leave is more acceptable than: Either you must pay up or leave, and: You can have either red wine or white is more acceptable than: You can either have red wine or white.

When either is a pronoun, it refers only to two things or people: Has either of you two seen Harry? For three or more things or people, use any. But when either is a conjunction, it is perfectly acceptable to use it for three or more things or people: For the first course, you can have either soup, pâté or fruit juice. As an adjective, either can mean either 'one or the other of two': She can write with either hand or 'each': There's a lifeguard station at either end of the beach. But be aware that when you use it in a context which could have both meanings, you may cause confusion: if you say, There's a service tunnel that runs on either side of the main tunnel, do you mean that there is one service tunnel that runs first on the left side of the main tunnel, then on the right, then on the left, and so on, or that there are two service tunnels, one on each side of the main tunnel.

HAS