Hi Laurel,
OK, I have some good news and bad news. The good news is that I had no problem connecting to your Eventbrite account and displaying events on my own test site.
The bad news, is that this means there’s something specific to your website that interferes with authenticating. Whether it’s on your side or Eventbrite’s side, I’m not sure; the links look right, and by changing nothing but the redirect URI (which is correct) in the applications (under eventbrite.com > accounts > app management), I can get my test site to connect successfully. Yours is the only case I’ve seen of this situation.
This all leads me to believe that there may be a plugin on your site that’s interfering with something (I noticed you have a few other event plugins also running). At this point, you would need to disable all other plugins and change to a default theme, to see if the problem clears up. If so, then change the theme back, then and back plugins one by one until you can replicate the problem (and know what plugin is responsible). All of which, of course, is incredibly time-consuming and disruptive.
If you pursue this course, keep me informed. Otherwise, you may be better sticking to one of your other event management plugins, if you’re not having problems with them.