The mechanic is in the NFHS Official's Manual.
There is no rotation. The lead coming across the key is not to force the Trail to switch sides.
When the ball, on the Trail side of the key, drops below the free throw line extended, the Lead can jump to the far side of the key and watch the impending post play/jockeying. When the jockeying stops or the ball goes back above the free-throw line, the Lead goes back to the other side of the key.
When the lead jumps across, they should take a position near the lane line, maybe a step more, looking back through the key, between the jockeying players - not towards the ball.
If the ball is passed into the post, now the Lead is in great position and it is his primary call.
IT is not like 3-man. No rotation; Trail stays where he is at.
It is a great mechanic. And should be used. The lazy veteran mentioned in the original post should retire. At a minimum he should quit perpetuating obsolete, poor mechanics to younger officials.