Get a volt meter and measure voltage drops in series with the circuit. Incrementally test connections from the battery to the load. You'll find voltage where there shouldn't be and drops that are unreasonably large. When you feel good about the switch, fuse, connector, etc, check the ground.
Best way to check ground is to get a jumper cable and connect it to the negative post of the battery. Then you can measure ground voltage at various places including the light harness. If you see more than a 0.020 volts drop anywhere, be suspect.
Bad connections will play off each other also. For example, the switch might have been less resistive than the fuse. But when the fuse was replaced, it's resistance went down significantly. Then when the circuit is activated, the switch which was good enough before, turns out to be the weak link. Kind of like fixing christmas lights.
Be on the lookout for corrosion, heat, and voltage drops. You'll definately find it.