Can my employer require me to clock out when there are no patients for me to serve and back in when there is?

Whether or not a practice such as this is permissible depends upon whether, and to what extent, your employer exercises control over you during the time you are clocked out. For example, if you are free to leave the premises and attend to personal business during the time you are clocked out, it probably is okay. If, however, you are required to remain available for work (for example, if you must stay at the office in case an emergency patient comes in), then, depending on the circumstances, your employer might be required to pay you for this time. The law makes a distinction between someone who is "engaged to wait" and someone who is "waiting to be engaged." The employer must pay the first person, but need not pay the second.

Of course, I would need more specific information from you regarding your employer's practices before I could give you a more definitive answer.