How do you search for a post by custom taxonomy?

For the record I found an answer to this question in the end – I needed to use a meta query rather than a taxonomy query. The correct code ended up being this:

$relatedBlogPostArgs = array(
    'post_type' => 'post',
    'post_status' => 'publish',
    'posts_per_page' => 1,
    'order' => 'DESC',
    'orderby' => 'date',
    'meta_query' => array(
        array(
            'key' => 'brand_post_link',
            'value' => $brandData->term_id
        )
    )
);
$relatedBlogPosts = new WP_Query($relatedBlogPostArgs);