> Are there some kind of boxes to plug on an RJ11 with two outgoing RJ11 >> plugs, that can tell if an incoming call is voice or fax, and direct >> the call to the ad hoc plug, either a handset or a fax-modem?
If you can get "distinctive ringing" for multiple numbers on a link there are boxes that will direct the call based on the ring pattern. This means the line doesn't get answered by the wrong machine which then has to "hand off" the call.
Multi-Link has one I've used for years. About $100 at Graybar.