An agent is not able to change their presence while in an on-duty state as shown below. It will show they are on duty and the presence drop-down list will not be clickable.
An agent will only be able to change their presence once they toggle their status to off-duty. This will allow you to click the drop-down list and select your presence as seen below.
Below is a list of all selected presences that are available when the agent is off-duty.