A hotter draw or load by certain types of halogen lights (e.g. foglites or driving lites) requires heavier circuitry hardware (switches, wires, etc.) to hande the extra load. This in itself is not a problem, simply put in the heavier wire and away you go. Picture a grade 10 electrical shop high school task, where you have to construct a basic circuit:
battery (+ side) -> wire-> switch-> wire-> light-> wire going back to-> battery (- side).
Now your existing Mustang headlight circuit is basically this, but on a scale suitable with regular headlights, with some additions like marker lights that we don't need to get into.
Now upgrading your headlights to units with a heavier draw: To visualize this, imagine the better pulling power of a 750 cfm versus a 450 cfm carb, you'd want bigger displacement, better manifolding, lumpier camshaft, bigger valve size, freer exhaust to take advantage of the bigger carb.
So it is with a heavier set of lights, or air horns, or whatever exterior electrical accessory, you reinforce the hardware to take it.
So rebuild your circuit , right? Well, your car already has stock wiring for the headlight circuit. It's silly to rewire the whole circuit with upgraded wiring. So how to reconcile the need for heavier wiring with the stock wiring we have?
Solution: add a relay.
The relay uses the above high school example, but after the new heavier wire you install leaves the Batt + side or other switched on pwer source, a "left turn" is inserted instead of the switch in the high school example. This "left turn" is called a relay, and to one of its four or five terminals (both are common) you attach a normal car gauge (14 or 16 gauge is fine IIRC) trigger wire, and it runs from the relay to whatever you wish to use to turn on your new lights. It can be connected to another circuit (parking lights if you wish) or a new switch you put in the dash, or whatever source you wish to use that when it is turned on it will tell the headlights to go on also. This is called a trigger circuit. You then run a light gauge wire back from this trigger switch back to the relay, one of the terminals on the relay will be for this return wire.
In the high school example above, this all functions as the switch, but does so using the lighter gauge, existing car wiring you have in your Mustang. You install the heavier gauge (12 is good) wire for the rest of the high school example - that is, your new lights. The rest of the relay terminals - one (or possibly two, on a five prong relay) go to the lights directly. all using the new haevier gauge wire, and the remaining terminal goes to a good ground like the frame or negative terminal of battery.
Two benefits of all this: 1) heavier circuitry will properly run your better lights, with excellent results, and 2) no new heavy or hot currect carrying wire will enter the driver's compartment.
I did all this with a set of Cibie Super Oscar driving lights with 100 watt bulbs on my old VW - I measured those suckers as they lit up the road for 7200 feet- and for 14 years never had an overheated wire or problem or output issue.
[/SIGPIC]67 Fastback GT -- original colour (Frost Turquoise), orig engine. Pic is of me and the Mustang taken in summer of '67, with original F70-14 Wide Ovals. Same car is now restored to "as new" but 3 speed tranny swapped out for 4 gear, with tach dash, original Equalock rear, Opentracker UCA, LCA, roller perches and idler arm, with roller bearing pedal cluster, Cibie headlights, 4100 carb (old 4300 put in storage probably forever)