I don't see why you couldn't.
Match the wires by their color codes and splice them together with splice connectors and a crimping tool.
First test to make sure it's not the headlight it's self that is broken then check for an shortage or cut in wires if no you can cut wires strip the plastic outline that protects it and put the right colored wires back together if not take it to a mechanic and get new wires
Cut the wires on the old fixture and splice wires from new receptacle
Cut the wires then splice on new socket
simply cut the two wires then splice the new ones on
cut both wires that run to the sensor and splice them together.
It could be, or a conductor [wire] that carries electrical current to the headlight could be cut or disconnected, or the headlight contacts in the lighting switch could be corroded or damaged from overheating.
alot of people like the look of them up so they pull the relay out so check the fuse box on your driver side under the hood. also the headlight button has wires running to it and often the brown wire is cut
bad ground or wire connection somewhere could be shorted too or bad headlight if its immediate would say wiring trydisconecting plugs from headlights and see what happens
you could have some faulty wiring. take your dash board off and see if any wires are frayed or broken
Simple, trace two thin white wires from the column down towards the firewall, it should connect to a two pin harness with orange wires. Measure the ohms resistance of your key and then cut wires and splice in a resistor of the same value
The answer to your question is ... None of the wires. if you cut any of the wires it will make the headlights malfunction and the pcm (The cars computer) will sense this and turn on the nortorious "Service Vehicle Soon" light or the MIL (Malfunction Idicator Light)