Excellent, Courtney! Thanks so much for setting me on the road to solving this problem!
The css line you provided (which I put in the widget-calendar.css file located in the /themes/Divi/tribe-events/pro folder) now correctly turns the date background blue if the events list widget is placed in the footer (and, I assume, sidebars). It still has no effect on the default dark gray date background when I insert the [tribe_events_list] shortcode to produce a similar list in the body of a main page column text/html. How to I control the colors in the little event list generated by the shortcode that’s not in a sidebar or footer?
Thanks!