Modifying the default search widget

I’m creating a plugin widget that does a different search from the normal default search widget. I copied the code from the default widget:

class new_search extends WP_Widget {


             function __construct() {
                    $widget_ops = array('classname' => 'widget_search', 'description' => __( "A search form for NextGen photos") );
                    parent::__construct('search', __('NGGSearch'), $widget_ops);
            }

            function widget( $args, $instance ) {
                    extract($args);
                    $title = apply_filters( 'widget_title', empty( $instance['title'] ) ? '' : $instance['title'], $instance, $this->id_base );

                    echo $before_widget;
                    if ( $title )
                            echo $before_title . $title . $after_title;

                    // Use current theme search form if it exists
                    get_search_form();

                    echo $after_widget;
            }

            function form( $instance ) {
                    $instance = wp_parse_args( (array) $instance, array( 'title' => '') );
                    $title = $instance['title'];
    ?>
                    <p><label for="<?php echo $this->get_field_id('title'); ?>"><?php _e('Title:'); ?> <input class="widefat" id="<?php echo $this->get_field_id('title'); ?>" name="<?php echo $this->get_field_name('title'); ?>" type="text" value="<?php echo esc_attr($title); ?>" /></label></p>
    <?php
            }

            function update( $new_instance, $old_instance ) {
                    return;
            $instance = $old_instance;
                    $new_instance = wp_parse_args((array) $new_instance, array( 'title' => ''));
                    $instance['title'] = strip_tags($new_instance['title']);
                    return $instance;
            }





    } // end class example_widget
    add_action('widgets_init', create_function('', 'return register_widget("new_search");'));
    ?>

I’m having trouble finding where this default search widget calls the search.php function. Basically I want to create my own search.php function (AKA searchNew.php) and call it when the user hits search. Any ideas where search.php is called so I can replace it with a different file?

Edit: I’ve looked in the searchform.php file already (the one called by get_search_form) and nothing there seems to suggest it’s calling search.php

You can hook into the ‘get_search_form’ action hook ( check out the “last option” part of the link below ). Set the priority high enough to override anything created in a theme.

A plugin could look like ( from the link below ):

function my_search_form( $form ) {
    $form = '<form role="search" method="get" id="searchform" class="searchform" action="' . home_url( "https://wordpress.stackexchange.com/" ) . '" >
    <div><label class="screen-reader-text" for="s">' . __( 'Search for:' ) . '</label>
    <input type="text" value="' . get_search_query() . '" name="s" id="s" />
    <input type="submit" id="searchsubmit" value="'. esc_attr__( 'Search' ) .'" />
    </div>
    </form>';

    return $form;
}

add_filter( 'get_search_form', 'my_search_form', 100 );

http://codex.wordpress.org/Function_Reference/get_search_form#Theme_Form