What Haywood says is correct. Both the talker and listener are both positive and need their own grounds. If the purpose of connection is only to receive GPS
and AIS, then you only need to connect the listener (Green) and a ground. But since AIS is high speed baud and GPS isn’t , this will be a problem. Likely will only get GPS.
EDIT: woops, I misread your post. If you want to get the AIS and GPS from VHF to the multiplexer, then you don’t need to connect listener at all. Just the talker and ground. But there may be two separate talkers. One for high speed AIS and one for GPS.