Skimmer should be ON for 24/7.
In my understanding "overskimming" is production of white, not concentrated foam. This can happen due to wrong adjusted air flow regulator of venturi. Skimmer should be adjusted so, that foam concentrates and only then being pushed up into the collection cup. The scum in the collection cup should be dark green to black color.
So i say definitely leave the skimmer ON for 24/7. Except skimming, protein skimmer enriches water with oxygen which is good for healthy reef environment.