I don't think this is possible. The only way I can imagine something similar is to divide the content where you want to place the search to 2 columns. One with 33% and one with 66% width. Place the search shortcode to the left column (33% width) and place the settings shortcode to the right column (66% width). More about shortcodes here.
Then I would set the settings to be visible by default, set the switch to invisible and the layout position to block: https://i.imgur.com/yYlXC5O.png
The code would look roughly something like this:
<div style='float:left;width: 31%;padding: 0 1%;'> [wpdreams_ajaxsearchpro id=1] </div> <div style='float:left;width: 62%;padding: 0 1%;'> [wpdreams_asp_settings id=1 element='div'] </div> <div style='clear:both;'></div>
This is just a very quick example.Best,
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