You are thinking of the pak sao as a parry (he throws a punch and you bat it away, like cuffing in boxing) -- it's not. This is not WCK's method.
The movement you describe (in the first section of the SNT) is not really a pak sao (although many mislabel it since it has the "shape" of a pak sao): it is a "supporting palm" and is generally used after you are already in contact.
To give you an example, your opponent has attached to you with a neck grabbing hand with his right hand. You want to get your left arm inside to regain control but his elbow is (correctly) down and in so that you have no room. You use this movement by quickly pushing his elbow "outward" with your right hand as you thread in your left arm (tan sao).