Please try JCE MediaBox 2.1.10 Beta - https://www.joomlacontenteditor.net/downloads/mediabox/development

This will allow you to create a popup link that will open a Mediabox popup automatically when the page loads after a delay of x seconds.

For example:

<a href="https://en.wikipedia.org/wiki/Cassiopeia" type="iframe" class="jcepopup" data-mediabox="1" data-mediabox-width="800" data-mediabox-height="600" data-mediabox-title="Cassiopeia" data-mediabox-caption="Mother of Andromeda" data-mediabox-autopopup="multiple" data-mediabox-delay="10">Cassiopeia</a>

using the data-mediabox-autopopup="multiple" and data-mediabox-delay="10" attributes will open a popup each time the page loads after a delay of 10 seconds.

You would need to use some javascript on the page to do this. Here is some example code (thanks to ChatGPT):

// Wait for the page to fully load
window.addEventListener('load', function() {
    // Find the link with the desired href
    var targetHref = 'http://example.com'; // Replace with the actual href you're looking for
    var links = document.getElementsByTagName('a');

    for (var i = 0; i < links.length; i++) {
        if (links[i].href === targetHref) {
            // Open the link in a new tab after a 10-second delay
            setTimeout(function(link) {
                window.open(link, '_blank');
            }, 10000, links[i].href);

            break;
        }
    }
});