Custom Taxonomy Basic Permalinks Not Working

I have a custom taxonomy called “location”. The pretty permalinks work great, and end up being something like myurl.com/location/term. Which is great.

But I’m trying to create a dropdown term list, and the only code that seems to meet my needs results in a link like this:

myurl.com/?cat=10

Now, normally I assume this would redirect to the correct location. I have no idea why it’s not. Instead, I get a “page not found.”

How can I make this work? I’ve tried enabling and disabling “rewrite” in the taxonomy registration, but nothing helps.

And of course I have reset all the permalinks plenty of times. How can I fix this?