Quizlet is the only source I've been able to find endorsing the extension of the proximity rule to correlative conjunction constructions used as subjects in interrogative questions:
When either and neither act as correlative conjunctions (when they are
paired with "or"/"nor"), the subject closer to the verb determines if
the verb singular or plural.
- Neither the principal or the teachers are at fault.
- Has either the president or his staff commented yet?
The argument that 'his staff' might be afforded singular agreement anyway by those disfavouring logical agreement does not really hold up as then the example would be inappropriate; the intention is obviously to pair a singular form NP with a plural form NP as in the first, declarative example. Admittedly, using 'staff' which can inherently regarded as either singular or plural in concept and correspondingly be afforded either agreement by those using logical agreement (and afforded singular agreement anyway by those opting for formal agreement) softens the incongruity of say
- Has either the king or the millions of people he rules voiced an opinion?
I'm not saying that Quizlet is as authoritative as say McCawley, but I'd certainly agree with what they recommend, and note the corresponding well known rule for interrogatives with normal disjunctive strings:
- Has the president or his staff commented yet?
- Has John or his brothers shown up yet?