I have had the same problem on two different trucks. One truck was shorting out through the reverse light switch wire which was damaged from a tranny swap. The second truck was blowing fuses due to aged/coroded trailer wiring from the tail lights to the plug on the bumper.
When the TS fuse blows, does your brake lights still work?
It seems to me the short is in the switch or or the front end. If the short is in the tail section, The brake light fuse would be blowing too because both brake and turn signal use the same wire, the function is based on the position of the TS switch.
Good thing to check would be the light pigtails in the grill, and wouldn't hurt to check the reverse wiring, maybe try unplugging the reverse switch for giggles.
Good luck!