What sort of wire should I use to connect additional lamps?
It depends on the bulb rating. Supposing you want to fit lamps which use 55 Watt bulbs.
Two bulbs will use 110 Watts of power. If the battery voltage with the engine running is 13.5 volts (typical) then the current required by the bulbs together will be Amps = Watts/Volts
= 110/13.5
= 8.15 Amps
So the minimum current rating of a wire feeding both lamps should be 10 Amps.
Since wire has a small but significant resistance, there will be a tiny voltage drop across it, so using thicker wire (say 20 Amp rated) might make the bulbs a fraction brighter.
In any case, the turn-on surge will be about 20 Amps because a bulb filament has a lower resistance when it is cold. Its resistance increases when it becomes white hot and it then takes less current. So, to cope with the turn-on surge while still protecting the cable in the event of a short-circuit, there should be a fuse rated at 20 Amps next to the battery. This will be the feed to the relay needed by the additional lamps.
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