Surely the antenna cable plugged into the VHF is the antenna your VHF uses to transmit!
You say that your Garmin aerial is connected to an NDC4 multiplexer (whatever that is), and then leads on to your VHF, but are there any other wires connected to the multiplexer which lead off in some other direction away from your VHF. It would be unusual and probably counter productive to have two satellite antennas both connected to the VHF, but quite possibly the Garmin satellite antenna provides the signal to both your VHF and also to your chart plotter, and if the antenna you are talking about is connected into the same place as that used by your Garmin satellite aerial, then it's highly likely that it is this wire that connects to your chart plotter. Each instrument does not need its own dedicated satellite aerial, all it needs is a signal which it can use and share with other instruments, so maybe you don't have a Raystar satellite aerial.
