Yes, use inversion. Cambridge Dictionaries website says:
When a clause with neither or nor is used after a negative clause, we invert the subject and the verb after neither and nor.
It gives one example with neither and one with nor:
He hadn’t done any homework, neither had he brought any of his books to class.
We didn’t get to see the castle, nor did we see the cathedral.
Further examples of sentences with "never" can be found in this question: "Nor" in combination with "never:" Usage and meaning. These also, in conjunction with the above, justify the validity of "Never ... neither ...", although this is not the question here.
Hence, it is fine to write:
I have never seen him laugh, neither have I ever seen him lose his temper.
Although using "nor" might be more usual.