I don't think there is a way, the action fires every time it's activated.
Yea I haven't found any relevant function regarding this. Is there any other Tableau features that can be used as a workaround?
No way to restrict it.
Yep, nothing in Tableau. I would suggest setting up some logic on the mail server side. if you have no access to this, then rather than using mailto: , you could just use a url action that goes to a server of yours where you can control the logic and determine when to send the email.