I would prefer to have a link at the top of the tag list saying "Advanced Tag Search" or something along those lines, and have that go to a page where one could do proper Boolean searching, either by having a single long box in which one could type tags separated by "and," "or," "not" (can we do "not"? I don't remember); or else as a series of individual boxes into which one could type the tags, separated by dropdown boxes for the "and" and "or" (and if possible also "not"). This second suggestion would look something like the advanced search page many libraries offer, such as this example from the Hennepin (MN, USA) County Public Library. We wouldn't need the first dropdown field shown there, since we would be searching in tags only, but the rest is similar to what I'm envisioning.
Thought of it