Customizer search with fuzzy-search from fuse.io. Created as a reply to https://wordpress.stackexchange.com/questions/287572/manipulating-customizer-panels-and-fields?noredirect=1#comment425917_287572

class-customizer-search-section.php

<?php
/**
 * A search section.
 *
 * @package     Customizer Search
 * @subpackage  Core
 * @copyright   Copyright (c) 2017, Aristeides Stathopoulos
 * @license     http://opensource.org/licenses/https://opensource.org/licenses/MIT
 * @since       1.0.0
 */

/**
 * Expanded Section for search.
 */
class Customizer_Search_Section extends WP_Customize_Section {

	/**
	 * The section type.
	 *
	 * @access public
	 * @var string
	 */
	public $type = 'customizer-search-section';
}

customizer-search.php

<?php
/**
 * Plugin Name:   Customizer Search
 * Plugin URI:    https://aristath.github.io
 * Description:   Adds search capability for customizer controls.
 * Author:        Aristeides Stathopoulos
 * Author URI:    https://aristath.github.io
 * Version:       1.0.0
 * Text Domain:   customizer-search
 *
 * GitHub Plugin URI: aristath/customizer-search
 * GitHub Plugin URI: https://github.com/aristath/customizer-search
 *
 * @package     Customizer Search
 * @category    Core
 * @author      Aristeides Stathopoulos
 * @copyright   Copyright (c) 2017, Aristeides Stathopoulos
 * @license     http://opensource.org/licenses/https://opensource.org/licenses/MIT
 * @since       1.0.0
 */

// Exit if accessed directly.
if ( ! defined( 'ABSPATH' ) ) {
    exit;
}

if ( ! defined( 'CUSTOMIZER_SEARCH_PATH' ) ) {
    define( 'CUSTOMIZER_SEARCH_PATH', dirname( __FILE__ ) );
}

if ( ! defined( 'CUSTOMIZER_SEARCH_URL' ) ) {
    define( 'CUSTOMIZER_SEARCH_URL', plugin_dir_url( __FILE__ ) );
}

/**
 * Add the section.
 *
 * @since 1.0.0
 */
function customizer_search_add_section( $wp_customize ) {
    
    // Include the section class.
    include_once wp_normalize_path( CUSTOMIZER_SEARCH_PATH . '/inc/class-customizer-search-section.php' );
    
    // Add section.
    $wp_customize->add_section( new Customizer_Search_Section( $wp_customize, 'customizer_search_section', array(
        'title'    => esc_attr__( 'Search', 'customizer-search' ),
        'priority' => 1,
    ) ) );
    
    // Add setting & control.
    // These are simply dummies because a section without controls is not displayed.
    $wp_customize->add_setting( 'customizer_search', array(
        'type'              => 'theme_mod',
        'capability'        => 'edit_theme_options',
        'default'           => '',
        'transport'         => 'postMessage',
        'sanitize_callback' => '__return_empty_string',
    ) );
    $wp_customize->add_control( 'customizer_search', array(
        'label'    => esc_attr__( 'Search Controls', 'kirki' ),
        'type'     => 'text',
        'section'  => 'customizer_search_section',
    ) );
}
add_action( 'customize_register', 'customizer_search_add_section' );

/**
 * Print scripts in kirkicustomize_controls_enqueue_scripts.
 *
 * @since 1.0.0
 */
function customizer_seach_kirkicustomize_controls_enqueue_scripts() {
    wp_enqueue_script( 'fuse', plugin_dir_url( __FILE__ ) . 'assets/js/fuse/fuse.min.js', array( 'jquery' ) );
    wp_enqueue_script( 'customizer-search', plugin_dir_url( __FILE__ ) . 'assets/js/script.js', array( 'jquery', 'fuse' ) );
    wp_enqueue_style( 'customizer-search', plugin_dir_url( __FILE__ ) . 'assets/css/styles.css' );
}
add_action( 'customize_controls_enqueue_scripts', 'customizer_seach_kirkicustomize_controls_enqueue_scripts', 9999999999 );

script.js

/* global Fuse */

var customizeSearch = {

    /**
     * All the controls with labels & descriptions.
     *
     * @since 1.0.0
     */
    controls: [],

    /**
     * Go through all controls and populate this.controls.
     *
     * @since 1.0.0
     */
    controlsInit: function() {
        var self = this;

        wp.customize.control.each( function( control ) {
            if ( control.id ) {

                self.controls.push( {
                    label: control.params.label || '',
                    description: control.params.description || '',
                    id: control.id
                } );
            }
        } );
    },

    initSearch: function() {
        var self = this,
            input = jQuery( '#customize-control-customizer_search input' ),
            wrapHTML = '<div class="customizer-search-results"></div>',
            options = {
                shouldSort: true,
                tokenize: true,
                findAllMatches: true,
                threshold: 0.4,
                location: 0,
                distance: 100,
                maxPatternLength: 32,
                minMatchCharLength: 1,
                keys: ['title', 'description']
            },
            fuseInit = false,
            searchVal;
        input.on( 'change paste keyup', function() {
            if ( ! fuseInit ) {
                fuseInit = new Fuse( self.controls, options );
            }
            searchVal = jQuery( this ).val();
            if ( 1 > jQuery( '#customize-control-customizer_search .customizer-search-results' ).length ) {
                jQuery( '#customize-control-customizer_search' ).append( wrapHTML );
            }

            // Clear previous results.
            jQuery( '#customize-control-customizer_search .search-results' ).empty();

            if ( 2 < jQuery( this ).val().length ) {
                _.each( fuseInit.search( searchVal ), function( result ) {
                    jQuery( '#customize-control-customizer_search .customizer-search-results' )
                        .append( '<span class="search-result" data-id="' + result.id + '">' + result.label + '</span>' );
                } );
            }

            jQuery( '.search-result' ).click( function( e ) {
                e.preventDefault();
                wp.customize.control( jQuery( this ).data( 'id' ) ).focus();
            } );
        } );
    }
};

jQuery( document ).ready( function() {
    customizeSearch.controlsInit();
    customizeSearch.initSearch();
} );

styles.css

#customize-theme-controls .control-section-customizer-search-section .accordion-section-title,
#customize-theme-controls .control-section-customizer-search-section .customize-section-back,
#customize-theme-controls .control-section-customizer-search-section .customize-section-description-container,
#customize-theme-controls .control-section-customizer-search-section .customize-section-title {
  display: none;
}
#customize-theme-controls .control-section-customizer-search-section.customize-pane-child {
  position: relative;
  visibility: visible;
  height: auto;
  margin-left: -300px;
}
#customize-theme-controls .control-section-customizer-search-section.customize-pane-child h3 .customize-action {
  display: none;
}
#accordion-section-customizer_search_section {
  border-bottom: 1px solid #ddd !important;
}
#customize-control-customizer_search {
  margin-bottom: 0;
}
.customizer-search-results .search-result {
  padding: 3px 0;
  border-bottom: 1px solid #f2f2f2;
  display: block;
}
.customizer-search-results .search-result:last-child {
  border-bottom: 0;
}
.customizer-search-results .search-result:hover {
  cursor: pointer;
  color: #35BAF1;
}

file structure:

customizer-search.php
inc/class-customizer-search-section.php
assets/js/script,js
assets/js/fuse/ - Copy the fuse.js & fuse.min.js files from http://fusejs.io/ in here.
assets/css/styles.css

It needs a few CSS and usability tweaks depending on the use-case, but it's 100% functional.