Though not popular in our state, we teach the 2-person ball-side mechanic to our lower level and new officials in our little corner across the lake from where Rut lives. It gives the rotated Lead a better look at the slot between low post players on the other side of the lane from their new position on ball-side. Otherwise, they'd be straightlined on verticality plays across the other side of the lane.
Also, when they transition to 3-person games we don't have to teach them how and when to rotate--they already know.
Besides the explanation in the NFHS Officials Manual, our state's online mechanics manual illustrates this mechanic according to the attached slide.
One caveat we issue: if the Lead rotates across only to put two eyes on the competitive matchup that Trail already is covering, don't waste the effort. If the Lead rotates across, he better be getting a better look at the competitive matchup(s) that the Trail can't handle. Otherwise don't do it.
2-Person Ball Side Mechanic: MHSAA Online Officials Manual