Amend behaviour on a Genesis Content Archives select setting toggle, to also show the related content limit setting when a different option is chosen.

admin.js

jQuery(function ($) {

	// Remove default Genesis behaviour for this select element.
	// If Genesis switches to using on() instead of live(), replace with a similar call
	// to off() instead of die(). The genesis event namespace only added in Genesis 1.8.0
	$('#genesis-settings\\[content_archive\\]').die('change.genesis');

	// Add in our behaviour, using multiple namespaces to try and play nicely with others
	$('#genesis-theme-settings-posts').on('change.genesis.my_theme_or_plugin', '#genesis-settings\\[content_archive\\]', my_theme_or_plugin.toggle_settings);

});

// Create the function in an object variable to namespace it.
var my_theme_or_plugin = {

	toggle_settings: function (element) {

		// Cache the limit setting selector, and the chosen option value
		var $limit_setting = jQuery('#genesis_content_limit_setting'),
		setting_value = jQuery(element.target).val();

		// Show the limit setting when needed for our value AND the Genesis value.
		if ('my-new-value' === setting_value || 'full' === setting_value) {
			$limit_setting.slideDown('fast');
		} else {
			$limit_setting.slideUp('fast');
		}
	}

}

functions.php

<?php

add_filter( 'genesis_archive_display_options', 'my_theme_or_plugin_add_content_archive_display_option' );
/**
 * Adds new option to display type in Genesis Theme Settings Content Archives box.
 *
 * @since 1.0.0
 *
 * @param array $options Existing display types.
 * @return array Amended display types.
 */
function my_theme_or_plugin_add_content_archive_display_option( $options ) {

	$options['my-new-value'] = __( 'Display X then Y and Z', 'my-theme-or-plugin-domain' );
	return $options;

}

// Remember to add a function that enqueues the admin script for this page!