On the discussion page of While or Whilst:

'Again, neither of these rules is well supported, and while and whilst are interchangeable in this meaning too.'

Rules is?/are? more than one, why then should it not be "are"?

'neither' is a pronoun and determiner. It is the subject of your sentence, not 'rules'.
The rule is, when 'either' and 'neither' are subjects, they always take singular verbs.

Neither of them is available to speak right now.

Either of us is capable of doing the job.