My courses limit the total access time to the course which counts down the time instead of up. But it’s the same thing as what you want just in reverse. I set a persistent variable called MasterTime and give it a value in seconds equivalent to the total time that they can access. Then on every page I put an action group that has one action that reduces the MasterTime variable by one. Finally, there is an action in the root of every page that runs that action group on an interval of 1 second. So every second, the MasterTime variable is reduced by one second which keeps time for what I want to accomplish.
One last thing. People can simply go to a page and let it sit for an hour which would count down the time without them doing anything. So I set an individual timer that counts down 10 minutes and resets on every page. If on any given page that timer reaches zero, I take them to a “timeout” page which has an action to reset the bookmark to the previous page visited, adds back the time that has been sapped by sitting on the previous page for 10 minutes and then closes the course after 60 seconds. Again, you can do the same thing in reverse.
Hope this helps.