Hi, Robert.
We love hearing about stuff like this, but we don’t have an API for events at this time. I believe you’re requesting the same thing as one of our existing feature requests: https://tribe.uservoice.com/forums/195723-feature-ideas/suggestions/15114291-wordpress-rest-api
Please do add your vote there.
This allows us to gauge interest in this particular feature request, which helps us prioritize our development efforts.
If it helps, though, our Events, Organizers, and Venues are 3 separate custom post types, and this extension (its GitHub link) might be helpful in knowing how to get some of the data from each event from WordPress custom fields, such as event start and end times.
I know this probably isn’t the answer you were hoping for, but maybe it helps your project move along a little bit…
Please let me know how things go for you.