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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.

Garris