You are correct, the light bar will draw 5.4 amps at 13.8 vdc or 6 amps at 12 vdc. According to the switch specs, there is no integral fuse. The spec does say the switch is rated at 20 amp.
Concerning wire size, 16 gauge automotive wire is large enough for 6 amps considering the distance that you will be running the wire. If you want to oversize the wire, you can use 14 gauge.
Concerning using a relay. The light bar only draws 6 amps which is not much and the switch is good for 20 amps. Even allowing for some safety factor, you will be working the switch at less than half of its design load capabilities. No need for a relay.
Now for the inline fuse. YES you want to install an inline fuse. You can install the fuse holder in the power feed to the switch. Concerning amp rating for the fuse. A 10 amp fuse will protect the circuit. The 16 gauge wire will handle 10 amps in the length of wire that you will be using. The switch is rated for 20 amps. So, the 10 amp fuse will protect the circuit from overload.
I believe you are confused as to how amperage in a circuit works. The amperage draw in a circuit is totally dependent on what load(s) are connected to the circuit, not the fuse or breaker size. In this circuit, the LED light bar is the only load and it will draw 6 amps, more realistically, probably 5.5 amps. It doesn't matter if you install a 20 amp fuse, the light bar will still only draw 5.5 - 6 amps.
Now, installing a 20 amp fuse will not protect the circuit from overload if a short circuit occurred, so you want to protect the circuit with a fuse that is based on the maximum allowed amperage of the smallest wire or switch ampacity in the circuit. In your case, that would be the 16 gauge wire. So, a 10 amp fuse would be what you want.
Be sure to make sure all your wiring connections are tight. Solder connections if possible. Solderless connectors will usually corrode over time which will cause voltage drop and increased amp draw. If I use solderless connectors, I also solder them after I crimp them on the wire.
Concerning wire size, 16 gauge automotive wire is large enough for 6 amps considering the distance that you will be running the wire. If you want to oversize the wire, you can use 14 gauge.
Concerning using a relay. The light bar only draws 6 amps which is not much and the switch is good for 20 amps. Even allowing for some safety factor, you will be working the switch at less than half of its design load capabilities. No need for a relay.
Now for the inline fuse. YES you want to install an inline fuse. You can install the fuse holder in the power feed to the switch. Concerning amp rating for the fuse. A 10 amp fuse will protect the circuit. The 16 gauge wire will handle 10 amps in the length of wire that you will be using. The switch is rated for 20 amps. So, the 10 amp fuse will protect the circuit from overload.
I believe you are confused as to how amperage in a circuit works. The amperage draw in a circuit is totally dependent on what load(s) are connected to the circuit, not the fuse or breaker size. In this circuit, the LED light bar is the only load and it will draw 6 amps, more realistically, probably 5.5 amps. It doesn't matter if you install a 20 amp fuse, the light bar will still only draw 5.5 - 6 amps.
Now, installing a 20 amp fuse will not protect the circuit from overload if a short circuit occurred, so you want to protect the circuit with a fuse that is based on the maximum allowed amperage of the smallest wire or switch ampacity in the circuit. In your case, that would be the 16 gauge wire. So, a 10 amp fuse would be what you want.
Be sure to make sure all your wiring connections are tight. Solder connections if possible. Solderless connectors will usually corrode over time which will cause voltage drop and increased amp draw. If I use solderless connectors, I also solder them after I crimp them on the wire.
