To take best advantage of oscillating shifts there must be at least two shifts in the leg.
Boats at 4 MPH VMG will sail the 0.5 mile, short, windward leg in about 8 minutes.
Therefore it is unlikely they will experience two (oscillating) shifts.
The last (or only) shift in a beat is a persistent shift.
In a persistent shift sail toward the shift first, as you become headed the layline will arrive soon. In west coast evening racing with a west wind and (persistent) westward shift; the best tactic is often to start right and tack on the header just before you reach the layline. You will be lifted to the mark.