Currently, my approach (thanks to so user help) is to load a offsite html into the current page via:

<script src="https://code.jquery.com/jquery-3.3.1.min.js"></script>   
<script type="text/javascript">
$(document).ready(function(){
    $("#output").load("https://homepageforme.com/pathtofile/Search.html");
});
</script>
    <div class="formClass">
        <div id="output">
        </div>

The only gripe I have here, is that this requires me to specifiy a full "url".

F.e. In iframes I could simply state "Search.html" (similar to a href), but here this won't work.

If there is no other workaround, I'd be ok with "taking the current window url" (window location) (sans the final file of the current page) => https://homepageforme.com/pathtofile/

then adding the fileanme "Search.html"

getting "https://homepageforme.com/pathtofile/Search.html"

that way and being able to feed it to the JS like this.

The reason being, that if I want to migrate the website, I'm forced to edit the paths manually.