Including taxonomy in searches

First you want to make the query keys available so you can check them later:

add_action( 'init', 'custom_add_query_vars' );
function custom_add_query_vars() {
    add_query_var( 'location' );
    add_query_var( 'tag' );
}

Then you want to set a tax_query by filtering the WP Query:

add_filter( 'pre_get_posts', 'custom_search_tax_query' );
function custom_search_tax_query() {

    // check this is a search query with post type of 'listings'
    if ( is_search() && get_query_var( 'post_type') 
    && ( get_query_var( 'post_type' ) == 'listings' ) ) {

        // check for location query var
        if ( get_query_var( 'location' ) ) {
            $location_query = array(
               'taxonomy' => 'location',
               'field'    => 'slug',
               'terms'    => get_query_var( 'location' ),
            );
        }

        // check for tag query var
        if ( get_query_var( 'tag' ) ) {
            $tag_query = array(
               'taxonomy' => 'tag',
               'field'    => 'slug',
               'terms'    => get_query_var( 'tag' ),
            );
        }

        // create the tax_query array
        if ( isset( $location_query ) && isset( $tag_query ) ) {
            $tax_query = array( 'relation' => 'AND', $location_query, $tag_query );
        } elseif ( isset( $location_query ) ) {$tax_query = array( $location_query );}
        elseif ( isset( $tag_query ) ) {$tax_query = array( $tag_query );}

        // finally set the tax_query
        if ( isset( $tax_query ) ) {$query->set( 'tax_query' => $tax_query );}
    }
}

Then you should be fine to pass the inputs from your search form to the keys location and tag and get the responding posts you desire. 🙂

Notes:

• There is no need to return $query from the filter as it is passed by reference.
• Strange as it may seem, the double-nested array of $tax_query is actually correct to allow for the relation argument – whether relation is set or not.
• Be careful with tag, if you are actually using the standard tag taxonomy it will need to be changed to post_tag (the taxonomy name for standard tags) in $tag_query, but here I assume you have added an extra taxonomy actually called tag.