"What colour is the copper inside the wire? "
Well, if the wire looks like copper rather than silver (tinned) then it is time to condemn the wiring
and replace it with proper marine-grade tinned wiring
. Somewhere in the circuit to the stern light, there's a loose or corroded contact or bad piece of wire. Either in the hot side, ground side, or socket, but somewhere there's a simple physical problem dropping the voltage.
Could be some yoyo twisted wires together and taped them over, instead of making a proper splice too.