Many tray (menubar) apps on OS X have different behavior on click and right-click.
Some don't show a menu when clicked, but instead changes the icon and does an action, but shows a menu for eg. Preferences and Quit on right-click:
Normal:

Clicked:

Right-clicked:

Unfortunately there isn't a built-in method to do right-click directly on a NSStatusItem, but it's easy to achieve it with a custom view. There's a handy library that handles it for you: https://github.com/heardrwt/RHStatusItemView
It should probably also trigger the right click event on Option+click.
This might be possible on Linux/Windows too, I haven't researched, but I'm interested in OS X support.
Many tray (menubar) apps on OS X have different behavior on click and right-click.
Some don't show a menu when clicked, but instead changes the icon and does an action, but shows a menu for eg. Preferences and Quit on right-click:
Normal:
Clicked:
Right-clicked:
Unfortunately there isn't a built-in method to do right-click directly on a NSStatusItem, but it's easy to achieve it with a custom view. There's a handy library that handles it for you: https://github.com/heardrwt/RHStatusItemView
It should probably also trigger the right click event on Option+click.
This might be possible on Linux/Windows too, I haven't researched, but I'm interested in OS X support.