I had some issues with my SH GX2150
VHF, and the Lowrance HDS-5m plotter. Now this might be more relevant than you think at first glance, as the Lowrance has singled-ended connections, while the GX2150
VHF has double-ended, just like your setup.
The - connections at the SH are inverted versions of the + output. They are not intended to be grounded. They should either be left floating, or tied to ground with a resistor.
So I think your cable arrangement should be :
White NMEA In (+) to Blue NMEA Out
Green NMEA Out (+) to Brown NMEA In
Orange & Yellow NMEA In/Out (-) unconnected
VHF ground to
Garmin ground
In the case of the latter, there should either be a shield on the
VHF's output cable, or you'll have to use a chassis ground.
I too found a lot of misinformation on the interweb, including from Lowrance support, but in the end asked a PhD electronics engineer at work, how to connect single ended to double ended. He told me to do it like above, and it worked straight away.
Right now it's not working because those - connections aren't ground. Therefore, the circuit is not complete. You need a complete circuit for current to flow / data to be transferred, and for that you need to complete the ground.