Custom Email Signup Registration Form

You can modify the custom auth/email signup registration page with the following steps (note this is a minor customisation to core code):

In auth/email/auth.php add the following code to call a custom signup form file:

function signup_form() {
	global $CFG;

	require_once($CFG->dirroot.'/auth/email/signup_form.php');
	return new login_signup_form(null, null, 'post', '', array('autocomplete'=>'on'));
}

This creates a hook to open the new file you will be creating auth/email/signup_form.php thereby minimising customisations to the existing auth/email plugin code.

Copy signup_form.php from login/ into auth/email.

Modify auth/email/signup_form.php accordingly.