I’ve been taught that when wiring junipers, to leave the wire on until it begins to bite into the branch. The guideline I was given that the bite should be as much as 1/3 of the wire diameter. 

Does this recommendation hold for the Hinoki Cypress as well? Or is it different and if so, how? 

I would not leave the wire on until it bites no matter species. Those ugly bite marks is visible for years.

I remove mine as soon as it looks like it’s going to bite into the branch. If it starts to bite I’ll remove and rewire on a different line. 

The wire bite scars will take forever to get ride of if you wait till 1/3 

yes 30% deep is very deep, far too much. Some scarring is ok especially on Pines but not recommended on deciduous trees. Best thing is to watch and remove when it starting to bite.

Thank you all for your replies. This is just what I was looking for.