Bigbug I think it should. As soon as you read the ticket and start on thinking of the next step the clock is running.
If you navigate away the timer still runs, which is also OK because you may want to check a document for an answer or link to share.
But if you are going to return to it later, a button that pauses and returns you to the ticket dashboard is useful.
I also had a new idea. In the top navigation bar, side menu, wherever, if a ticket timer is running, there is a timer icon running with the elapsed time.