Adding File Type Form Field to Drupal System Theme Settings

I'm trying to add a "file" type field to my theme's settings. I'm not using a base theme and am working in Drupal 7. The field shows up in the correct place and I can select a file, but, when I save the settings, the file does not show up in my files folder and running theme_get_settings on the setting returns an empty string. What am I doing incorrectly?

Here is my field code:

// footer settings
$form['footer_settings'] = array(
    '#type' => 'fieldset',
    '#title' => t('Footer Settings'),
    '#collapsible' => TRUE,
    '#collapsed' => FALSE,
);
$form['footer_settings']['footer_logo_path'] = array(
    '#type' => 'textfield',
    '#title' => t('Footer Logo Path'),
    '#default_value' => theme_get_setting('footer_logo', ''),
);
$form['footer_settings']['footer_logo'] = array(
    '#type' => 'file',
    '#title' => t('Footer Logo'),
    '#description' => t('Upload a new logo image to be displayed in the footer of the website here.'),
    '#upload_location' => file_default_scheme() . '://',
);

When you use a file form control, you have to add a validate and a submit method (or modify the existing ones) to upload the file itself.

You can have a look at the default system theme method, witch allow you to define the favicon and the logo files to use with your theme : => In the file /modules/system/system.admin.inc

...
    $form['logo']['settings']['logo_upload'] = array(
      '#type' => 'file',
      '#title' => t('Upload logo image'),
      '#maxlength' => 40,
      '#description' => t("If you don't have direct file access to the server, use this field to upload your logo.")
    );
...
  $form['#submit'][] = 'system_theme_settings_submit';
  $form['#validate'][] = 'system_theme_settings_validate';
...
/**
 * Validator for the system_theme_settings() form.
 */
function system_theme_settings_validate($form, &$form_state) {
  // Handle file uploads.
  $validators = array('file_validate_is_image' => array());

  // Check for a new uploaded logo.
  $file = file_save_upload('logo_upload', $validators);
  if (isset($file)) {
    // File upload was attempted.
    if ($file) {
      // Put the temporary file in form_values so we can save it on submit.
      $form_state['values']['logo_upload'] = $file;
    }
    else {
      // File upload failed.
      form_set_error('logo_upload', t('The logo could not be uploaded.'));
    }
  }

  $validators = array('file_validate_extensions' => array('ico png gif jpg jpeg apng svg'));
...
  // If the user provided a path for a logo or favicon file, make sure a file
  // exists at that path.
  if (!empty($form_state['values']['logo_path'])) {
    $path = _system_theme_settings_validate_path($form_state['values']['logo_path']);
    if (!$path) {
      form_set_error('logo_path', t('The custom logo path is invalid.'));
    }
  }
  if (!empty($form_state['values']['favicon_path'])) {
    $path = _system_theme_settings_validate_path($form_state['values']['favicon_path']);
    if (!$path) {
      form_set_error('favicon_path', t('The custom favicon path is invalid.'));
    }
  }
}
...

/**
 * Process system_theme_settings form submissions.
 */
function system_theme_settings_submit($form, &$form_state) {
...
  if (!empty($values['logo_upload'])) {
    $file = $values['logo_upload'];
    unset($values['logo_upload']);
    $filename = file_unmanaged_copy($file->uri);
    $values['default_logo'] = 0;
    $values['logo_path'] = $filename;
    $values['toggle_logo'] = 1;
  }

  // If the user entered a path relative to the system files directory for
  // a logo or favicon, store a public:// URI so the theme system can handle it.
  if (!empty($values['logo_path'])) {
    $values['logo_path'] = _system_theme_settings_validate_path($values['logo_path']);
  }
...
}

Edit

As I said in the comment below, you must save the file received in the 'footer_logo' combo, and populate the 'footer_logo_path' value with the path of the saved file.

  // If the user uploaded a new logo, save it to a permanent location
  if (!empty($values['footer_logo'])) {
    $file = $values['footer_logo'];
    unset($values['footer_logo']);
    $filename = file_unmanaged_copy($file->uri);
    $values['footer_logo_path'] = $filename;
  }

Then it will not be a trouble if the methods are running twice.