You are most welcome, I’m glad I was able to help you in this matter. There is no obligation but by your kind words I wonder if I could trouble you to leave a review based on this experience here:

https://wordpress.org/support/plugin/add-search-to-menu/reviews/?filter=5

I’d really appreciate that. 🙂

And if I can be of any further assistance please don’t hesitate to ask.

Could you please share me the page URL from your site where it is displaying so that I can help you?

I hope you are well today and thank you for your question.

The search results page is displayed by the search.php file of the theme that you are using on your site so the plugin doesn’t control how the search result will be displayed on the search results page but your site theme controls it.

You can change this developing custom code in the search.php file of your child theme by contacting the theme author or consider hiring a developer to develop it for you. You can hire a developer from any freelance site or WordPress agency.

You can also consider us to develop it for you using the form https://ivorysearch.com/custom-work/

Best regards,
Ivory Search Support

I logged into your shared site and confirmed the issue which seems some type of conflict issue.

I have resolved the issue now by adding the below CSS code in the Custom CSS option of Ivory Search plugin settings on the path Ivory Search -> Settings -> Settings

li.is-menu.dropdown:hover > form {
    display: block;
}

li.is-menu input.assistive-text.searchsubmit {
    clip: unset;
}

li.is-menu path {
    fill: #FFF;
}

That type of dropdown search form only works in the menu so could you please display it in the menu so that I can help you to change search Icon solor to white and make it work?