Add a Email field to the WordPress Customizer.

WP Customizer - Email

$wp_customize->add_setting( 'themeslug_email_setting_id', array(
  'capability' => 'edit_theme_options',
  'default' => '',
  'sanitize_callback' => 'themeslug_sanitize_email',
) );

$wp_customize->add_control( 'themeslug_email_setting_id', array(
  'type' => 'email',
  'section' => 'custom_section', // Required, core or custom.
  'label' => __( 'Custom Email' ),
  'description' => __( 'This is a custom email input.' ),
  'input_attrs' => array(
    'placeholder' => __( 'email@domain.com' ),
  ),
) );

function themeslug_sanitize_email( $email, $setting ) {
	return ( is_email($email) ? $email : $setting->default );
}