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To get the button, the ticket must be assigned to you ๐
If I remember correctly, time tracking is meant for the agent working on the ticket, so it needs to have an agent assigned to work.
Just in case you have not seen it: You can click on the little question mark on the top-right of any form in an app and it will open the application help page. It includes chapters for the features of the current app, like the ticket system.