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Hello @sixaxis !
Thanks for reaching out.
The left search sidebar is a theme-specific design. In all of our premium themes, you are going to have the sidebar at the left in the All listing page and the Search result page.
To implement the instant/Ajax search option you have to navigate to Directory Listings> Settings> All listing
Then turn on the instant search option.
Even if you do not have the search sidebar at the left, the instant search should work.
Kind Regards.