Image appearing at random times while running other events

I need a little help here. I have a simple task, the user, after a random interval, has to click 1 button to make it dissappear and appear somewhere else. THAT is already working, what I’m having trouble with is that I need an image to randomly appear for a moment (a second or less) WHILE the user is doing the described task. It is very important that the image doesn’t appear as a consequence of the user clicking the button it just has to be random.

What can I do here?

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