GoDaddy's Website Builder (part of GoDaddy Websites + Marketing) product is not a supported platform for the FullContact webtag.
While GoDaddy's Website Builder product provides their customers with the option to insert a custom HTML code block, this section of HTML is embedded in the page in an iframe in the of the page, isolated away from the rest of the page.
The FullContact webtag must be installed in the source of all of the pages that you want to recognize visitors. It is currently not possible with GoDaddy's Website Builder product to install javascript in the page source - a limitation imposed by GoDaddy.
In older versions of GoDaddy's Website Builder product (ver. 6 + earlier), there were fields in Settings that would allow users to embed custom code in both the header and footer of a website. GoDaddy removed that ability when they transitioned customers to the newest version of the Website Builder product.
For GoDaddy's Website Builder product for building websites, there are not other options.
If you have another GoDaddy product that allows you to edit the source code of your website, you may be able to use the FullContact webtag. Reach out to support@fullcontact.com for additional guidance or suggestions.