Not quite the answer, but I think you can catch the context menu on the button. (I do not know the events from my head). If you can catch the context menu, click on the button, then it will be the same as the right click.
BUTTON down is not a good way. A click will only be caught when the user makes the button up. Try to press the button and, before you take your finger away from the button, disconnect the mouse from it. At the same time, there is no upward recording for this button, as well as a click.
Again, I know this is not the answer, but that might be the key. I’m a pocket guy, so most often I don’t have a “right mouse button”.
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