If you're able to use the History Change event, then that means the dropdown is causing the browser's navigation history to be updated every time the dropdown is opened and/or closed. So every time the navigation history gets updated, the History Change event gets triggered, and your Rule runs accordingly.
Furthermore, it sounds like you want to the dropdown open to be tracked for the first time only, and not subsequent times. To limit the number of times that the Rule runs, you can consider using the Core > Max Frequency condition: