According to the rules you are not allowed to initiate an action, which does not have the capacity to change the game state.
With that in mind, is there a consensus regarding such an action like investigating your location, when it does not have any clues on it but you want to make pay-offs for the FBI-agents weakness? Along those same lines, could he also use his character ability to pay off said weakness, when there are no clues present?
If he can then he would be able to get rid of his weakness relatively easy by seeking out the lowest valued shroud locations with no clues and if he cannot then it would be an autoloss for him when a scenario has progressed far enough that there are no more clues left.
Been following the grim rule so far but would be nice to have it put to rest.
Bonus question: lead investigator can change between scenarios of the same campaign or meant to be the same?