Various answers don’t give an answer I’ve been able to use.
With numpad emulation on (blender 2.9) if I map shift + numpad 1, shift + numpad 2, and shift + numpad 3 to the select mode, it acts like Ctrl + mouse click, on the icon. In other words, to switch between vertex and face, I have select face then deselect vertex, otherwise they are both selected. Is there a way to change this so each is exclusive?