How do you schedule the right to take a week off each semester?
This is the exact wording from my studio policy:
The schedule for each semester, including weeks that there will be no lessons, is posted on the website (here) and included in the September newsletter each year.
At the beginning of each studio year I figure out my schedule and make note of what weeks I’ll be traveling or taking breaks. These are reflected on the studio calendar. The additional week off mentioned in the policy is primarily in case I am sick or have another emergency that prevents me from teaching. In theory, I could just take off the week if I wanted some time off, too, but I’ve never been able to bring myself to do this. So usually, my students just benefit from that extra week each semester. 
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Great wording! I’ve been wanting to implement such a thing into my policy, and now I know how. Thank you!
As a school music teacher who also teaches private lessons, I’ve never had a moral issue with not teaching lessons during the normal school breaks. I won’t teach lessons during Spring Break, and will only teach during Christmas vacation upon request if I’m available. I tend not to take much time off from either my school teaching or my private lessons, but if I need the occassional mental health day (which I need but rarely take!) I try to do it at a time that will not inconvenience people. If students have auditions or performances coming up, I make every effort to teach.
Don’t feel guilty about taking time off when you need it. People understand.