either . . . or: agreement
The verb after either . . . or and neither . . . nor.
When both subjects are singular, the verb is singular: Either the clerk or the guard has the key. When the subjects differ in number, the verb agrees with the nearer subject: Either the clerk or the files are missing. Either the files or the clerk is missing.
Examples
Use Either the note or the file is gone.
Use Either the note or the files are gone.
Avoid Either the clerk or the guard have the key.