Either or Neither in sentence with another negative

It is not true that nor can only occur in sentences that also involve neither. But this is still quite a different proposition from trying to pair it up as either..nor instead of as neither..nor.

Consider this valid sentence and why it works:

I have never visited England, nor have I ever visited Scotland either.

Please see this answer for copious citations from the OED, literature, and other sources including:

• But it was never published (though some indication of its content could be gleaned from The Lord of the Rings), and throughout my father’s long life he never abandoned it, nor ceased even in his last years to work on it.
• I could not find her, nor even the crimson-shot orange disk of the old sun.
• And he would never walk, nor fly, nor be a knight.
• It has never been that way, nor is it now.

Most speakers today would say:

I have never visited England or Scotland.

But you could also get away with writing:

I’ve been to Wales a few times before via the quick jaunt across the Irish Sea, yet to this date I have never visited England — nor Scotland, come to think of it.