Both alternatives might be found, but both present problems. The advice of ‘The Cambridge Guide to English Usage’ in such cases is to rewrite the sentence in which the words occur. If, for example, you were faced with a choice between ‘Neither he nor I has ever been there’ and ‘Neither he nor I have ever been there’, it would be a simple matter to write the sentence as ‘He has never been there and neither have I.’
Here's the relevant extract:
Further options arise when the coordinates present a mixture of
grammatical persons, especially the first person singular:
Neither she nor I is? / am? / are? inclined to go.
The use of is (third person) sounds awkward after I (first
person), and am too is less than ideal: though it accords perfectly
with I and provides proximity agreement, it makes a disjunction
with she. Notional agreement would suggest are, to bundle she
and I up together as plural, first / third person, but it’s still
less than an elegant solution. Such sentences probably need
redesigning, for example: I am not inclined to go and neither is
she.