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Hi Patrick,
In short the GPS 'data out' goes to the VHF 'GPS +', GPS ground goes to ground, VHF 'GPS -' goes to ground.
Looking at the Garmin GPS60c manual, the 'data out' and 'data in' wires are the '+' signals for each while the power ground wire is the '-' signal. The Raymarine 54 VHF manual shows only 'NMEA in' connections but explicitly shows the polarity. As you suspected, you want to connect the Garmin 'data out' (brown wire) to the 'GPS +' (yellow wire) of the Raymarine 54 VHF and the ground of the Garmin (black) to the Raymarine 54 'GPS -' (green wire). The Garmin black wire will already be grounded if it is being powered from the boat dc distribution so only the Raymarine 54 'GPS -' (green) will need to be tied to ground. If you are running the Garmin off its internal batteries you will need to connect the Garmin ground (black) wire to the Raymarine 'GPS -' (green) wire.
I am basing the colours on what is stated in the manuals I just downloaded for those two units. Hopefully they agree with your manuals.
Ken
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