Howdy Jean,
I would love to help you with this.
I actually an example of adding a second taxonomy filter available:
https://gist.github.com/elimn/99bf67696bb3e1be85d9c4b0300314c5
My filter is not actually for a separate taxonomy, but rather it is the regular category filter styled a bit differently. But it should still prove pretty helpful in showing how best to add filters.
I started by extending <span class=”pl-e”>Tribe__Events__Filterbar__Filters__Category which is located in the-events-calendar-filterbar/src/Tribe/Filters/Category.php and I would recommend you do the same. In you case you would likely want to override the pre_get_posts() method in that function with one of your own. If I understand you right all you want to do is the change the taxonomy itself, so if you copy/paste the current method into you new class that extends the old (like my example) then just change the taxonomy in there you should be all set!</span>
Does that all make sense? Will that work for you? Please let me know.
Cheers!
– Brook