I'm afraid we don't have any specific tutorials or documentation for this specific sort of customization, but I believe it can be achieved by customizing the Swiftype plug-in as well as your theme.
One approach would be to assign unique IDs to the respective search inputs and then writing functions that specifically filter the search request depending on which ID is active.
We have some additional documentation here:
For more advanced customizations like this, you might want to consider migrating from the WordPress plug-in and implementing Swiftype Search via our web crawler or developer API.
Feel free to email us from the Support menu of the Swiftype dashboard with questions specifically related to your UTH engine.