My truck doesn't have an alternator of course so I am going to guess at what I think the problem is. I understand that the alternator has a connection to the ignition switch, which supplies voltage to allow the alternator to build up it's field, when the motor is first started. When the iginition is turned off, it probably takes a while for the alternator voltage to collapse. Normally the engine would stop first. So I think maybe the alternator is supplying voltage through that wire and somehow through the heater connection.
I would be inclined to disconnect the alternator somehow, and see if the problem still exists.
