Tie a (tennis ball) or boxing speed ball up higher than your head (smaller the ball the better for your vision and reactions.Make sure there is abacking board so the ball comes back to you straight away.
Get into a right front stance so your right leg and right arm are forward and punch at the ball continually over a few weeks and just throw the punch and take your hand back to the side of your chin and throw again from the chin only so the actions are continual.
This will train you into keeping it up.
then go into the other stance and throw from the rear with the right hand too just to balance you up. Then mix it up with both hands later and you'll find your right will right up there with your left at all times.