has_category applies only to default post type.
You are working on a CPT so you should use has_term()
if ( is_singular( 'eventbrite_events' ) && has_term( 'network', '{YOUR_CUSTOM_TAXONOMY}' ) )
where {YOUR_CUSTOM_TAXONOMY} is optional and it must be the slug for eventbrite_events taxonomy to which the term ‘network’ is attached to.