T680 Headlight Assembly

Do you have a projector as a low beam?

 

just a little fun fact incase you want more light or have issues with led fans burning out....

Bi-Xenon: Morimoto EVOX-R 2.0 - HID Projectors - Components

these morimoto evoxr 2.0 are a direct fit for your factory projectors and can be pulled out the back without opening the headlight. the evo has the best high beam out of any projector out there, pair it with a oem quality d2s bulb and a hylux ballast (all found on the site linked) and you'll have light output like you never imagined.

for a plug in led bulb, those opt 7 look pretty good too.

 

as for your wire burning issue, put a multimeter on it and measure resistance, I bet your over 1ohm on that ground which is why it keeps melting.

 

I can feel my retinas burning already.

 

Replace the connector and terminals with a Motorcraft Pigtail kit, WPT 1497 (HU2Z-14S411-KA) which has silver plated terminals and 14 gauge wire which can handle the high heat this bulb generates and overheats the terminals causing spread, loose terminals.

 

Truck wiring.