"In theory" it's supposed to be brown. But mine isn't wired to the standard, so don't be surprised if yours isn't, either.
If you can get to your umbilical cord Junction box, you can open it and see if the brown wire from the umbilical cord is connected to brown trailer wiring. Whatever color wire it's connected to, that's the color your running lights wiring is.
You might want to make sure that pin 3 of the 7-way connector is actually connected to the umbilical cords brown wire. A few folks have reported that their umbilical cord doesn't follow the standard either.
1988 Coleman Sequoia - popup (1987-2009) - outlasted 3 Dodge Grand Caravans!
2012 Roo19 - hybrid (2012-2015)
2016 Mini Lite 2503S - tt (2015 - ???)
2011 Traverse LT, 3.6L, FWD
2009 Silverado 1500 Ext Cab, 5.3L, 4x4, 3.73
2016 Silverado 2500HD Dbl Cab, 6.0L 4x4, 4.10