Automatic logout after leaving password protected area (WP)

I have a Wordpress site, and I have one page password-protected. The way this functionality is built is that Wordpress doesn't log the user out for a long time.

I need this to be changed so that the user is logged-out when the tab or browser closes, and also after a determined period of time (30 minutes would be ideal). The user should also not be able to hit the "back" button and have access to that page without re-entering their password.

The code you write must be cross-browser and platform compatible, and ideally it will be code which I can reuse on other sites.

I will not give you the Wordpress password for implementation on my site, so you will need to explain to me how to implement the code.

Clarification:
I figured out how to do this by editing the core file, but that change will be overwritten with each Wordpress upgrade. The solution you implement should be written in a more stable way than what I did.

If necessary I can give you WP access for this job.

PHP Arhitectură software WordPress

ID Proiect: #1089863

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