>>> Is there a different variable that should be used instead?
>>
>> I can't find another variable.  Maybe a new variable should be created,
>> with a name like next-error-current.
>
> Re-reading the code, we don't really need the variable at all.  The call
> to the highlighting function has been moved into the C-x ` command,
> after all, so we already know what buffer to use, and where point is.
>
> So I've now changed this to just highlight the current line in the
> "error buffer", which seems to work fine in the couple of use cases I
> tried.

Simplicity is the hallmark of truth :-)

Surprisingly, this feature works everywhere, even in diff-mode.
But when using next-error on an empty line in diff-mode, its highlighting
is too short to notice - only 1 character wide.  Maybe the next-error-message
face should extend to the end of the window like hl-line-mode face does?

I tried to add the attribute ':extend t' to the next-error-message face,
but it has no effect.  Maybe because currently highlighting is not added
to the trailing newline.  Indeed, with this patch it works: