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I A very well written explanation, GregThe Gen 1 Fog Lamps are standard H3 halogen lamps - 55w. Two on the circuit - 110w of current draw. 110w/12v = 9.17 Amps - call it 10 Amps including wire resistance. The fuse should be another 30% or more over the planned draw - so a 15 A fuse is correct.
It isn't an issue of supply, it is an issue of draw. The wires on the circuit should support 15 A of current - supporting a load of 180w. The car can supply as many Amps of current as is in the battery. But the issue is the draw of the device using the power. LEDs generally draw less power, depending on the LED type and the number of LEDs deployed on the lamp. Look at the wattage draw of the LEDs you plan to use. If they are over 90w of draw each, the wiring and the fuse are insufficient to carry the load and will fail over time.
If the LED lamps you want to use require more power than 180w in total, you have a minimum of two options:
1. Fish out all existing wires for the lamp circuit and replace them with wire one gauge lower - lower is larger. This would be a serious PTA and likely to break other things.
2. Run an auxiliary power feed from the fuse block to a relay, and use the existing circuit to provide a control circuit for the relay. Size the wire, relay, and fuse to support 150% of the planned load. If you have an empty fuse in the block, use it. Otherwise, run an inline fuse for the power circuit.
The headlamps on motorcycles in the 80's and 90's (heck, even later) were anemic 55w lamps. People would upgrade to 90w lamps to throw more photos down the road, burn out the contact on lamp switches, and sometimes burn out the wire harness itself. The trick was to run a circuit off the battery through a relay and use the existing circuit as the control circuit. If you put the relay in the headlamp nacelle the wiring was self-enclosed except for the lead back to the battery. Without raising the watts on the lamp, the extra volts pushed by the battery (13-14) would make a 55w lamp a bit brighter. However, the main reason for the conversion was to use 90w or 110w "offroad" lamps for "safety".