Send an email when a ticket with billable hours is closed?

Is there a way to do this?

Here's our scenario: most of the customers we have on support have some sort of support agreement with us, so we don't really need anything more than the reporting we can do on hours spent on tickets for them, etc.

But for a few customers, we only bill them for hours used in support. So, when we have a ticket for them that gets worked (and time gets applied to it), we would like to be notified (or have some easy way of being aware) when the ticket is closed, so that it doesn't slip through the cracks, and we know to bill them accordingly.

Is there a way to do this? A workflow rule perhaps? I've looked already (in the workflow rules), but couldn't see a way to do it.

Thanks,
Tim