Make sure that the LED assembly is square int he housing before you secure it.
Now pass the wires back through the gromet and then reattach the gromet to the stud. Don't forget about the green wire that you removed earlier from the stud. Make sure to reattach it between the two nuts on the stud.
Now, go ahead and cut the three wires for the original bulb socket, and strip them about .5" and do the same for the three wires on the LED assembly. Now before you crimp them together, make sure that you have your heat shrink in place on the wires. Now crimp (or solder) the wires together like this:
Original -->
LED
Brown -------->
Black
Black --------->
Green
Yellow/
Green -->
Red
Now before you reinstall the assembly, make sure that your turn signals, running lights, and brake lights all work. If any of them do not, retrace your steps and see where you went wrong. Once everything is working as it should, reinstall the sockets and their matching bulbs, then the tail light housing.
A quick test, just for kicks (this is witht he running lights on, not the brake lights or turn signals.
Reinstall the lens (A new lens is a REALLY good idea)
