Update: we use both Service Desk (classic JIRA project) and Kanban (also a classic project) and the “Start timer” hook-in is still there in the Kanban project, but not in the Service Desk project.
Update 2: I’ve worked out the difference. The hook-in doesn’t show when you’re viewing the ticket in the queue, but if you open the ticket directly then it does.
This does not show the hook-in: /jira/servicedesk/projects/ESD/queues/custom/45/ESD-6801
The does show the hook-in: /browse/ESD-6801
If the hook-in can be added to the queue-view of an item that would be helpful.