I played around with the product timers. I think that would be the best way to go. You could set it up when an menu item for the room is added to the ticket a product timer gets added as well (with a zero price). You will need an Add Order action, you will only need to fill in the Menu Item Name with the product timer. Then in Rules you would use a rule event of Order Added to Ticket and constrain it to the menu item(s) for the room(s) and add the new action.
The user would stop the product timer when the customer was done with the room. It would show how much time has elapsed and the user could add what ever charge for going over the hour limit.
Using Product Timer you have built in printer templates options: