Calling custom PHP from a HTML form post action gives 404 error

Add unique field in your form.

Eg: <input type="hidden" name="wdm_action" value="1">

Put your 'customer-details.php' file code in below function:-

 add_action('template_redirect','wdm_customer_details'){
//check if that field present in the form, if yes then perform the action
if(isset($_POST['wdm_action'] && $_POST['wdm_action'] != ''){
    //customer-details.php file code

}
    }