Hi @BrianCCampbell ,
There is no such out of box property to show the visible status of Calendar Tab, and the Cancel button doesn't trigger anything, so it's a little tricky.
As an alternative workaround, I accomplish your needs by a TextInput box, Calendar icon, and a calendar component.
Please find the calendar component in the attachment.
1. import the calendar component into the app
2. add a TextInput box, Calendar icon, and a calendar component
3. set App.OnStart: Set(MyVar,false)
3. set Text box.Default: Calendar_1.StartDate
4. set icon. OnSelect: Set(MyVar,true);Set(selectedDate,Calendar_1.StartDate)
5. set OK Button.OnSelect: Set(MyVar,false)
6. set Cancel Button.OnSelect: Reset(Calendar_1);Set(MyVar,false)
7. set rectangle.Visible: MyVar
Test Result: 
Hope this helps.
Sik