Dear Bjoern,
You can set for advanced search in params layout - default and you will have below view
ordasvit.com/joomla-vehicle-manager/inde...46-13/search-default
If you want hide items for rent in search you should use Search Module
for Vehicle Manager, You can show or hide different default parameters for search - category, rental availability, price (with moving slider), year of issue and much more.
In component search you could not make that
ordasoft.com/vehicle-manager-joomla-automotive-extension
Thanks,
Taras