You could use an action hook like tribe_events_before_template and use the is_archive() and/or is_tax() conditionals, like:
if ( is_archive() and is_tax( Tribe__Events__Main::TAXONOMY ) ) { /* do something here */ }
I hope this helps point you in the right direction.
If there’s a code snippet you’d like me to put some eyes on or something else I can help you with, please update this ticket or create a new ticket if it’s a separate issue.
Thank you very much for your understanding.
If you need some coding help, you may want to ask your developer or reference our documentation and list of known customizers.