Actual reverse polarity can exist either on the dock or on-board your own vessel. It does not matter where the reversing point is, on the dock or on-board, both scenarios will energize the reverse polarity indicator and create a potential for shock hazard.
With a faint RPI light you don't likely have a real reverse polarity situation but still could so check with a tester first. It is much more likely to be a voltage drop / resistance issue if the dock and polarity test well.. However if an older neon type light is used then it may just be weak and you could still have a reverse polarity situation. Reverse polarity testers are very inexpensive at Home Depot or Lowes.
The ABYC requirement for reverse polarity indicating lights is that they use minimum 25k Ohm Resistor. This is so they "indicate" at below the 5mA that a standard US spec GFCI will trip at. In the old days the indicator lights were neon based and for the last 20 or so years they have been LED but all should have a 25k Ohm resistor in the circuit.. This light sits between the AC white/neutral and AC green/earth ground and responds to a reversal of the ungrounded (black) and the grounded (white) conductors .
Keep in mind that when Muffy and Skippy fire up the brand new Sea Ray, untie the dock lines, and steam away from the dock forgetting about the power cord, it is usually Darrel the dock boy and his other buddy Darrel who re-wire the dock post. Don't trust them and start with a test of the dock post for reverse polarity. If you don't have a tester ask the marina to test it for you and be there to watch it..
It is possible for the reverse polarity indicator circuit to faintly illuminate even though the circuit is properly wired. This most often occurs from voltage drop but some inverters and even some battery chargers have been known to cause this as well. To test this you can simply disconnect your inverter or charger and see if the RPI is still faintly lit.
Thanks to a guy name Ohm, and his law, voltage is always consumed trying to push amperage through a wire. If the voltage differs between the beginning and end of the run or any two points in-between this is called voltage drop. Voltage drop can be caused by undersized wiring, improper or poor connections / terminations or corrosion. Bad or loose friction fits in shore power receptacles can also cause some VD or resistance. This difference is what can dimly illuminate a RP indicator light.
If you flip on a high amp draw load there can often be enough voltage drop along the neutral path to overcome the resistance in the 25,000 Ohm resistor thus lighting it faintly. Voltage drop is not as dangerous as sucking on live wires, but should be attended to if discovered.. Check all connections, use a tester, and make sure your AC input wiring from the dock to the panel are sufficiently sized for your loads. In some cases just trying a different dock pole and shore power cord can eliminate issues on-board and isolate them to the cord or dock post..
ABYC E11 - SHORE POWER POLARITY DEVICES
E-8.10.1 Reverse polarity indicating devices providing a continuous visible or audible signal shall be installed in 120 V AC shore power systems and must respond to the reversal of the ungrounded (black) and the grounded (white) conductors (See E-8.23.1, Diagram 3,)
E-8.10.1.1 the polarity of the system must be maintained for the proper operation of the electrical devices in the system,
E-8.10.1.2 a branch circuit is provided with overcurrent protection in only the ungrounded (black) current-carrying conductors per ABYC E-8.11.6.1
E-8.10.2 Reverse polarity indicating devices are not required in systems employing polarization or isolation transformers that establish the polarity on the boat.
E-8.10.3 The total impedance of polarity indicating and protection devices connected between normal current carrying conductors (grounded [white] conductor and ungrounded [black] conductor) and the grounding conductor shall not be less than 25,000 ohms at 120 volts, 60 hertz at all times.