How can I set up a rule somewhere that will automatically email the department head anytime one of their staff creates a ticket? I can see one for Service Requests but I can't make it work for tickets.
You could add a cc to the ticket with a dispatcher rule. Here's an example that might work.
But the department head will differ depending on who submits the ticket. In Freshservice there is a field for "department head" when you set up each department. And then you assign requesters to those departments. So logically I should be able to use that department head field when creating a rule for new incidents but that is not an option. I tried tweaking the approval rule for Service Requests since we won't be using SR approvals anyway and that's the only time I've seen "department head" as a send to option. It'll run anything else I put in that rule except sending the "approval" email to the department head.