You are required to add a single line of code if you wish to add validator on any other page which isn't a homepage.
Demo link: https://rbz-section.myshopify.com/pages/validate-zip-code
In following example, we will create a separate page for validation.
1. Go to App > Global Settings.
2. Change restriction type to be "Section (widget)"
3. Visit your stores admin panel.
4. Click on "Online Store" > "Pages" > "Add Page"
5. Click on "Show Editor" button and copy paste following code.
In this example, we are adding only validator. You can also add your custom text below and above validator.
<div id="rbz-zipcode-check-section"></div>
6. Save page and you should see validator on your newly created page.
If you would like to hide a page title, you can hide it using a Custom CSS available in app Design & Validator settings.