Though Safari doesn't save your browsing history during a private session, your Mac logs this information in the Terminal archive. You can access your private browsing history through the Terminal archive, but it might be a bit tricky as the website names are translated into their IP addresses. Here's a step-by-step guide:
- Click Applications > Utilities.
- Click Console > Your Mac HD on the sidebar.
- Type any:mdnsresponder in the search box, then click the Play button.
- Open another Finder window and click Applications > Utilities.
- Click Terminal.
- Type the following at the command prompt: sudo killall -INFO mDNSResponder
- Provide your admin password and press Return.
- Go back to the Console to see your Private Browsing History.
Remember, the exact website names won't be visible, only their corresponding IP addresses. I found this guide on The Mac Observer that could be helpful to you.