Either and neither are masters of disguise! They can be pronouns; and if so, they are always singular. Or they can be part of a two-part conjunction (either … or, neither … nor) joining two or more subjects. In that case, the verb must agree with the nearer subject.
In the questions below, decide whether either and neither are singular subjects, or conjunctions joining subjects. And when you’ve figured that out and you know what the subject is, pick the verb that agrees.