I found a an old TSB, that may be what you are referring to, however it does not apply to our trucks. It is an issue with the Front Control module which can present itself with weird lighting problems.
In going through the SM I saw the directional signals are tied to the FCM, so I looked up the part# and then Googled it on the internets. The park lamps are separate and have a fuse.
Here is the part# for the FCM, 56051036AD, it is what led me to the TSB. This is a $212 guess. I'm not a betting man...
I am not saying this is the problem. Dig around for a copy of the SM and look at the electrical section. You have to start testing for shorts to ground, f'd up wiring, etc. I would not spend $212 unless you're pretty damn sure that was the culprit.
http://www.Xkjeeps.Com/TSB/tsb_xk_0806005.Pdf