Setting `evil-ex-search-persistent-highlight` to `nil` does not clear highlight when pressing `n` or `N`

I've got `evil-search-module` set to `evil-search`.

If I set `evil-ex-search-persistent-highlight` to `nil`, the highlight (correctly) goes away when I conclude a search by pressing return. However, when I press `n` or `N`, the highlight returns and remains permanently. I'd like a way to configure this such that it has the same behaviour as isearch: when `n` is pressed, show the highlight until the cursor is moved. This could be implemented by changing how `evil-ex-search-persistent-highlight` behaves, or by adding a new configuration variable.