Magento 1 – Module Disabled in app/etc/modules Still Showing in Admin

A tab does not appear if you don't have sections in it (most probably).
Add a section with at least a group and a field in it.
[EDIT] Here is my system.xml that worked:

<?xml version="1.0"?>
<config>
    <tabs>
        <test_module translate="label" module="test_module">
            <label>Test Module</label>
            <sort_order>999</sort_order>
        </test_module>
    </tabs>
    <sections>
        <test_module translate="label" module="test_module">
            <label>Test</label>
            <tab>test_module</tab>
            <frontend_type>text</frontend_type>
            <sort_order>400</sort_order>
            <show_in_default>1</show_in_default>
            <show_in_website>1</show_in_website>
            <show_in_store>1</show_in_store>
            <groups>
                <settings translate="label">
                    <label>Settings</label>
                    <frontend_type>text</frontend_type>
                    <sort_order>10</sort_order>
                    <show_in_default>1</show_in_default>
                    <show_in_website>1</show_in_website>
                    <show_in_store>1</show_in_store>
                    <fields>
                        <enabled translate="label">
                            <label>Enabled</label>
                            <frontend_type>select</frontend_type>
                            <source_model>adminhtml/system_config_source_yesno</source_model>
                            <sort_order>10</sort_order>
                            <show_in_default>1</show_in_default>
                            <show_in_website>1</show_in_website>
                            <show_in_store>1</show_in_store>
                        </enabled>
                    </fields>
                </settings>
            </groups>
        </test_module>
    </sections>
</config>

1. System > Configuration > Advanced > Disable Modules Output will not actually disable that module. It work as the name suggest, disable modules output.

   When you look at

   abstract class Mage_Core_Block_Abstract
   

   In

   final public function toHtml()
   {
       Mage::dispatchEvent('core_block_abstract_to_html_before', array('block' => $this));
       if (Mage::getStoreConfig('advanced/modules_disable_output/' . $this->getModuleName())) {
           return '';
       } 
   
   // It is checking If its in disabled mode then just return blank output
   .......
   }
   

2. While app/etc/modules completely disabled module