The problem is often corrosion in the socket or on the base of the bulb. In case you haven't already done it, remove the bulbs and use a bit of fine sandpaper to clean the bulb's metal tip and brass sleeve. Then clean the inside of the socket, using a pencil to push the sandpaper around a bit. Good luck.
The voltage across the two leads of the switch was 3 volts? I don't know how this could be. If the switch is ON, there should be zero volts across the leads, and anything else indicates a bad switch. If the switch is OFF, no current is passing, so a skin grounding problem won't cause any voltage drop. In other words, there should be full battery voltage across these two leads. Was the switch on or off when you checked it?
Bill
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