This usersript will add an autocomplete to TVMaze (searches for Shows/People as you type) and can also optionally be used as a search history.
I contacted TVMaze about this, but after 3 weeks I still haven't received a reply so I'm not going to wait any more. The screenshot above just shows Show Search, but you can select to search for People instead. I've taken precautions so that this shouldn't cause issues for TVMaze's server (minimum 4 letters typed, only search after you stop typing for 0.5 seconds).
How to install
Firefox users: Download Greasemonkey
Chrome users: Download Tampermonkey
Go to the OpenUserJS script page
Click the blue 'Install' button on OpenUserJS and follow the on-screen instructions
All other tips/usage can be found on the OpenUserJS page