I would have bet a dollar that incandescent bulb would light dimly at 10 volts
I've seen corroded wire do crazy things though, you read voltage but it can't carry enough current to light a bulb
Thats where I would be moving the pos wire from the switch to a known hot terminal. then move the return to a known good neg terminal
wait a minute, this isn't one of those all-around lights on a post that plugs into a socket in the gunnel?
If it is, there is your problem! they are the red headed cousin to trailer lights
50% of the reason I paid $3k for a hard top was to have a place to mount a permanent hard wired anchor light...