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I have a 17' 1984 Montauk and am currently trying to restore the lights on the boat (bow and stern). I have tested the voltage at the battery terminals and it reads 12.4V, the battery is less than a year old, however there is a wire going from the battery to the console and when tested on the end of that wire it reads only 4.5V. I know that I need 12V for both of the lights and I have connected them both directly to the battery and they have turned on. Any suggestions would be fantastic.
Some voltage drop is expected with the use of any fixture/accessory. Yours is excessive. Heavily corroded connectors, poor attachments to the wire, tired switch, etc.... can all lead tho voltage drop. Disconnect the ends of the leads and buff out corrosion, see if the leads are held together by half the wires, if non shrink wrapped connections the resistance could be inside the crimp, see if tinned wire, etc..... It may very well be the wire but resistance could anywhere along the line of use. Start at the battery and work your way along. Ohm (resistance) testing gets complicated.
As an example....I came home to no water Saturday night with my well system. I started at the source at the service fuse box (110v), then opposite side of fuse (110v), then switch (good), then secondary fuse box.....one fuse had continuity but had a major voltage drop....replaced fuse still no water, upward to the splice area on top of the tank (my pump sits inside the holding tank)......one connection has a cut in the insulation and it slowly corroded/severed the connection, reattached the wires.....good to go (all the connections need revamping, lots of patina throughout). So......... on Saturday night I am thinking "....how do I get a new pump from a professional shop over Memorial Day Weekend......" with no sleep that night to installing a single twist connector. Do not jump to conclusions and worries of pulling new wire until testing done.
Have you checked the resistance of the wire from the source to the object its powering?
Is there a breaker in the circuit you are using? I had a breaker recently fail in its operating position. It was only letting out 0.5V. I isolated the problem only after hooking the electronic item directly to 12V and saw that it was working as expected.
Unfortunately, Whaler cheaped out on navigation light wiring for 30 years, running unprotected grey duplex wire directly in the boat tunnel, where it can easily get abraded and fail from other rigging work, forcing other cable through, etc. As mentioned, this is your problem.
In a Whaler floor tunnel, which end up filled with dirt and grime, wire should only be run that is Ancor boat cable, with white protective sheathing over the two encapsulated wires. Use 16/2.