Here is what I did. There is a light bulb in the ignition switch bracket which illuminates the the ignition key area when the headlights are on.
I cut the wire for that light and wired it to the "ignition-on" terminal of the ignition switch.
Now, when my Chinese-made ignition switch remains "on", in spite of the fact that the key has been turned to the "off" position and the key has been removed, the light reminds me that the ignition is still "on".
Carl