I guess customers will be customers, but this seems rather demented to me. I cannot fathom why a business would ever want to frustrate its potential customers by giving them the appearance that they are (too) "busy" to handle their call. Even if it is the off-season and a customer called, I would think that it likely that the customer would assume for the first couple of times that the line was indeed busy, but after a few attempts would get frustrated and take the business elsewhere.
In any event, you face a couple of issues:
1. The first is defining what is the on- & off-season. You did not mention how the calls will get to the Q, so I assume it might be an inbound trunk that connects directly. If that is the case, then you can create two Q, one for each season, and then simply switch to which Q the trunk will connect to with the inbound rules given the applicable season. It will require a manual change to direct, but minimal as I assume the switch to once to go off-season and again to go on-season. You might even be able to setup a dummy extension and have the trunk connect to the extension and using the status on the extension, away might point to in-season Q and out-of-office points to the off-season Q.
2. The next issue is the busy signal. By definition the functionality of a PBX is to allow for the efficient handling of multiple simultaneous calls so as to provide the caller with the best opportunity of reaching their intended recipient. The PBX really doesn't support a "busy" in the traditional sense. Somewhat like a cell phone, you either get the call, get vmail or get disconnected (rejected by the caller). You might be able to direct the call back to a digital receptionist and instead of the usual greeting, record 30 seconds or so of a busy signal (as the prompt) and then have no options as an input with the setting that should they push a number, the prompt is repeated and then the timeout is set for 30 seconds or so and then disconnect. I just don't understand why they wouldn't do the same as I have outlined with at least a message to indicate that it is out of season and the season will start at XXX, so please call back then or if needed push y to leave a voice mail.....but not my business.
3. With the analog line they can have a ring group which they can select which phones are members of same and then select a strategy to ring all. Depending upon the number of members, you may want to look at multicast paging. I am uncertain what you seek when you indicate - "they want a separate "line" button that shows up on all phones. Can a group of lines show up this way?" Can you elaborate? I get the part of a separate button on each phone, but I then lose the need when a "group" of lines show up this way. A single, separate button showing a group isn't resonating with me?
Phone System 