You can save yourself the trouble and stop looking. That wire won't exist.
I just looked in the schematics for the '02, '03, and '04 Excursions and SD's.
Looks like the Ex's back then were never equipped with marker light wiring for the mirrors, only turn signals.
I guess it's better to know...
I'll pull the Inner Door Cover off and see if the brown wire is on the "truck" side of the mirror connector. I'm pretty sure it is. The question then becomes if it makes it into the cab.
The park light circuit should be a brown wire in the CJB, or the brown wire coming off the back of the headlight switch.
I don't have a brown wire on the back of my headlamp switch. I mapped that out pretty well when I was ciphering on how to have my fog lamps always on.
[Jumper pins 2 and 12 - blows Fuse# 15 under hood, so pull it first]
Anyway, park lamps involve pins 10, 11, & 12 - with 10 being the "hot", IIRC.
So, I should be able to tie to 11 (since I'm already using 12) to fire the clearance lights. They are LEDs, so current draw should be negligible.