Hi Steven,
Anything is possible!
You could simply use WordPress’s existing widget_display_callback filter and change the instance properties accordingly – the basic form of something like this would be:
add_filter( 'widget_display_callback', 'customize_list_widget', 10, 3 );
function customize_list_widget( $instance, $widget, $args ) {
if ( 'tribe-events-adv-list-widget' !== $widget->id_base ) return $instance;
if ( ! tribe_is_event_category() ) return $instance;
// Insert your logic to set the category here, ie:
// $instance['category'] = 4096;
return $instance;
}
Do bear in mind though that some changes are afoot and the next release will incorporate a new way of specifying multiple categories/tags to filter the result set – rather as the calendar widget currently works – so you may need to adjust your solution at that point.
I hope that helps 🙂