Hi alfonsotesauro,
I has guessed that you forgot to click JAT3 cache after displaying the search module in Module Manager. That is why the search box still appeared. So, The simplest method is disabling the module in Module Manager + Clear JAT3 cache (The button is on the top right of dashboard).
With editing .php file method, you will see the php functions to call a search module in pluginssystemjat3jat3base-themesdefaultblocksheader.php file at line:
<?php if($this->countModules('search')) : ?>
<div id="ja-search">
<jdoc:include type="modules" name="search" />
</div>
<?php endif; ?>
Note: You shouldn’t use the editing .php file method because I will be not effective when you update new T3v2 version.