How to search for not null values?

[verdant-spark]

I'm trying to search through all customers in a store which has a lot of customers and want to exclude those with no email address. If I search using a URL such as: /customers/search.json?query=email:* then I get a correct set of results, however, when using the customer resource and search method I get all customers.

$query = 'email:*';
$customer_resource = $shopify->Customer();
   try {
       $customers = $customer_resource->search($query);
   }...

As an aside, the search resource can take a mixed param but the Customer resource declares it as a string (and so throws an IDE warning)

 * Customer -> Custom actions
 * --------------------------------------------------------------------------
 * @method array search(string $query = '')      Search for customers matching supplied query
 */

[verdant-spark]

(edited as I think I answered part of my own question, but then found a different problem...)