>> 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:
>
> Makes sense; go ahead and apply.

Now pushed.  After a day of using it, I realized this feature paved the way
to another very useful feature: when the highlighting overlay is not removed
after going to the next occurrence, and leaves the highlighting
on all visited lines, this provides an overview what lines were
already visited, and what lines not yet visited - like visited links
are highlighted differently in browsers.  This patch builds this feature
on the top of the initial patch: