Hi Kristen,
What you’ve described is the correct and expected behaviour of each shortcode.
[tribe_events_list] is, essentially, a ‘wrapper’ around our advanced events list widget. Just like the widget itself, it does not support the presence of the Tribe Search Bar.
[tribe_events] is used for embedding our full event views – there again, it imitates a normal view such as events/month or events/list, which also don’t have an organizer option as such.
However! There is a way. You can customize any of our views – the primary method for doing so being the creation template overrides – and the basic process is outlined in our Themer’s Guide:
theeventscalendar.com/knowledgebase/themers-guide
If you need the Tribe Search Bar, it would probably make the most sense to customize our list view templates so that they expose the organizer data you are interested in.
I hope that helps!