You have already checked the voltage and found it low, so the first thing I would check is any connections or wire splices going to the switch and the light. Corrosion or a poor connection can cause a voltage drop.
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Craig and Susan
Morgan Hill, CA 2007 Newmar Kountry Star 3910 towing a 1998 Ford Explorer. RVing since gas was 58 cents a gallon. Amateur Radio Operator (W6ADV) since 1962.
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