Taxonomy search block - Search for e.g. "mac" -> Go to URL /tags/mac I just want a simple "search" block for the tags taxonomy. It should work like I wrote in the title:

If you search for the tag "x", it should automatically go to the URL /tags/x.

I'm aware that it may result in "Page not found", but that's ok.

It's more like a "go to URL" block rather than a search.
You can use Custom Search module. This module allows you to manipulate search functionality.

It has sub module called custom search Taxonomy which allows you to search according to taxonomy terms.

This allows you to configure path also. 

If you want to use custom search paths, enter them here in the form path|label, 
one per line (if only one path is specified, the selector will be hidden). 

The [key] token will be replaced by what is entered in the search box, and the [terms] token will be replaced by the selected taxonomy term id(s).

Ie: mysearch/[key]/[terms]|My custom search label.