Hi Ryan.
You can enable SCRIPT_DEBUG to use the non-minified JS files.
Looking into the source, I see Line 209 of /wp-content/plugins/the-events-calendar-filterbar/src/resources/js/filter-scripts.js is the JS that resets the filters. The targeted ID gets set from one of the 2 files in /wp-content/plugins/the-events-calendar-filterbar/src/views/filter-bar/
That JS file gets enqueued at Line 206 of /wp-content/plugins/the-events-calendar-filterbar/src/Tribe/View.php
I’d guess the only way to customize that JS is to dequeue it and enqueue your own modified version.
Or (probably easier) you could just look at that JS function’s logic and piggyback/copycat it yourself to duplicate its functionality for your own custom inputs.
I hope that helps get you further along with your customization!
If you need some coding help, you may want to ask your developer or reference our documentation and list of known customizers.