Form with throbber not responding to validate or submit methods
According to the Drupal official documentation on drupal_build_form.


  method: The HTTP form method to use for finding the input for this form. May be 'post' or 'get'. Defaults to 'post'. Note that 'get' method forms do not use form ids so are always considered to be submitted, which can have unexpected effects. The 'get' method should only be used on forms that do not change data, as that is exclusively the domain of 'post.'


I would recommend you using POST method rather then GET method, so please remove the line $form["#method"] = "get";

Also, you should rewrite your ajax callback.

function hook_models_update($form, &amp;$form_state) {
   unset($form_state['input']['model'], $form_state['values']['model']);
   $brand = $form_state['values']['brand'];
   $brand_desc = "";
   $results = db_query("SELECT description FROM {taxonomy_term_data} tax WHERE tax.tid = :tid", array(":tid" =&gt; $brand));
    foreach($results as $row) $brand_desc = $row-&gt;description;

    if($brand_desc != "") $form['model']['#options'] =      _hook_list_models($brand_desc);
    unset($form['model']["#attributes"]['disabled']);
   $form['model']['#disabled'] = FALSE;
   $form["model"]["#attributes"]["id"] = "edit-model";

   $form_state['rebuild'] = TRUE;
   return $form['model'];
}


IMPORTANT NOTE:

If you can, I would suggest you rename your function or module name to avoid using hook_ prefix. It would cause unexpected function name conflict in future, because hook_ prefix is reserved for building hook API in Drupal.