According to this link, if at least one of the nouns involved is plural then it should take the plural form of the verb. Otherwise, it should take the singular form of the verb. But in the last part it says not all grammars agree to those rules thus proximity rule applies. However, it doesn't explain when to apply the proximity rule and when not to use the former rules.
The “proximity rule” you are referring to is that when you have a compound but disjunctive subject, the verb agrees in number with the closer — or in the case of three or more, the closest — of the subjects.
But it is often better to rephrase:
And then there was nor
This same rule applies (well, or can apply) to neither/nor sets as much as it does for either/or instances. So in all the examples just provided, you can change all instances of either into neither and of or into nor, and the verb remains unchanged. So:
All that being said, one can also find examples in writers of renown where neither is used with a plural verb despite both elements being singular themselves.