Hiya Phil,
NMEA has two types of devices, V1 and V2.
- V1 is dumb, it's a single TX (or RX) wire and a ground.
- V2 is smarter, it uses 2 wires and no ground.
The Garmin GPSMAP is a V1 device. The other two are V2 devices.
There are two simple rules when going between the two. For a:
- V2 Talker to a V1 Listener (GME to Garmin)....wire the + port to the Input port, and the - to the ground port;
- V1 Talker to a V2 Listener (Garmin to Raymarine)....wire the Output port to the + port , and the ground to the - port.
Here's a simple wiring diagram showing the correct way to wire between V1 and V2.
Hope this helps!

On yours, you should disconnect the blue wire (GME AIS Receiver) from the Blue wire (Garmin GPSMAP). The reason is:
The Blue wire on the GPSMAP is transmitting NMEA strings.
The Blue wire on the GME AIS is also transmitting NMEA strings. (This is the same signal as the GME Brown wire, just 180 degrees out of phase).
That's two transmitters talking at each other. Just connect the GME blue wire to the GPSMAP black wire and you da man!