Okay, tested CharacterSelected. It works well; using the trigger below, I removed the DoubleCombat1 trait by clicking on the general.

Code:
;------------------------------------------
Trigger CharacterSelected Test
    WhenToTest CharacterSelected

    Condition CharacterIsLocal
          and IsGeneral
          and Trait DoubleCombat1 = 1

    Affects AntiDoubleCombat1  1  Chance  100