Hi,
I have looked at the code via FTP in your theme directory, and I have made a quick possible solution for you, which you can customize now.
Please note, that this is not part of the regular support, so I cannot guarantee it will work properly at all times.
The code I have placed to the wp-content\themes\etechaim\views\templates\wp-search.php file is:
If you select a taxonomy, it will display the message with the taxonomy name as you described it, otherwise it will show the search phrase only.