The reading of 2V in one direction on the GI indicates that there is an open diode in that direction. The unit will not conduct AC fault current as it should, and should not be considered safe. However, it will still block galvanic current. A shorted diode will still conduct fault current but will not block galvanic current. These are the two failure modes.
The diagram attached shows the internal components, 4 diodes and a capacitor. The capacitor isn't important in the current discussion. Diodes have a characteristic voltage drop - applied voltage must exceed this level before the diode will conduct. Further, the diode conducts in one direction only, all current is blocked in the reverse direction. The nominal drop for a standard diode is aprox 0.6V, two diodes in series drop 1.2V, a little more than the range of galvanic voltages in sea
water, that's how the isolation is obtained. The galvanic current is DC and flows in one direction, so just one of the two strings of diodes provides the desired galvanic isolation, while both strings are involved with conducting AC fault current, one for each half-cycle of the AC. The capacitor conducts AC only and fills in the 1.2V gap so that all AC current will be conducted through the isolator.
The OPs observation with the GI test doesn't indicate that it isn't doing its job as far as isolating, but it does indicate that it may not conduct AC fault current effectively. However, I would repeat the test directly at the GI connections without involving the shore cord. The reason is that a false reading may have been obtained if the capacitor was not fully discharged between tests in each direction.
It would be most productive to further troubleshoot with galvanic potential readings taken with a multimeter and a reference probe made from a zinc pencil anode.