When signaling a corner kick should the referee always signal towards his closest corner? i.e. Never across the goal.

There is only one signal for a corner kick.  The Assistant Referee follows the ball down to the goal line.  The referee stops close to the goal area line but never past the corner flag.  The AR shows the flag at a 45 degree down angle.  The flag is never shown past the corner flag.  The AR does not indicate with the corner signal which side the Corner Kick should be taken as this is the referee's responsibility.

If you're asking about the Center referee's signal, or the signal of the Lead referee in a 2-man system:

The answer is the referees signal for a CK in a 3man or 2man system is to signal to the corner where the kick is to be taken.