The register button simply redirects the user to the standard Joomla registration page. We don't have a popup for that. You can simply create a standard link to the registration page.
If the SCLogin module is already shown on the page, you can create a link like below to trigger it's popup:
<a href="#login-modal" data-toggle="modal">Login with Existing Account</a>
I hope that helps, but if you run into any issues, just let me know.
Thanks,
Alex