Implicating to the Left or Right is straight forward as there are no decisions to be made. However, Implicating Across simply states the card will be moved to "a player not to your immediate Right or Left".
However, the rules are less clear on who determines the target of the implication. The Inspector physically moves the cards, but is it the Inspector or the player getting rid of the card who decides where the card is passed across?
Sorry if that did not come across clearly.
The player getting rid of the card decides which 'Across' player to target.