In order for you to track Agent Activity for a non-Zendesk user, you will first have to enable the Standalone Clock 
for your account and then add the non-Zendesk user.
Once you have enabled the Standalone Clock, agents that do not use Zendesk will be able to click on the icon on the top left of the tymeshift WebApp to Start and End their Day and Clock In and Out of General Tasks.
Do note that if you do not have any General Tasks created, the timer will show time tracked as Uncategorized Time.