Show Featured Image On First 2 Posts In Any Archive

This code removes or adds the featured image to the first 2 posts in any archive based on this question from a member of the StudioPress community:

I know that this is a strange thing to ask but as the Topic Title I would like to show the featured image only on the first two posts in an archive page. I’ve already used the option in the Genesis panel to show the post images in a page archive but I would like to customize it even more on specific page archives.

Here’s the visual:

Here’s the code for logged in members: