Whether an actor is a primary or secondary actor is NOT a diagram level distinction, it is per Use Case. An actor may be the primary actor of one use case, but secondary to another, so this 'convention' of left/right is not helpful unless you're duplicating actors (which is allowed). The Cockburn definition of a Primary actor is about whose user (sea level) goal is being achieved by the use case - who initiates it is not the definition. If I receive a notification on my phone - who initiates that (and don't you dare say 'time' as an actor? When I view the notification I get the benefit/value from it and achieve my goal of reading it. Are there one or two use cases there? It depends what you find useful to model - there is NO absolutely right answer (remember, "all models are wrong, but some may be useful").

Whether an actor is a primary or secondary actor is NOT a diagram level distinction, it is per Use Case. An actor may be the primary actor of one use case, but secondary to another, so this 'convention' of left/right is not helpful unless you're duplicating actors (which is allowed). The Cockburn definition of a Primary actor is about whose user (sea level) goal is being achieved by the use case - who initiates it is not the definition. If I receive a notification on my phone - who initiates that (and don't you dare say 'time' as an actor)? When I view the notification I get the benefit/value from it and achieve my goal of reading it. Are there one or two use cases there? It depends what you find useful to model - there is NO absolutely right answer (remember, "all models are wrong, but some may be useful").