Very easy
Engineer a click-box incorporating a small actuator, which is powered by a dc motor. Add controller. Code it to activate a period of lets say 15min.
Plug in power, position keyboard, do some testing and let the magic happen.
Optional: install a web-cam to monitor if you still online and let it push-notify you over app, when you got logged out in order to adjust the period.
... Tooo easy man
How do I know this will work? Well, please find my record of functional sketches below:
https://www.imgur.com/jninS9Q.png