It is "possible", but what you would need to do is:
1) Create a media query for the toggle using hidden-phone or something similar. If you Google "Joomla hide on mobile" or something like that you should get a few articles on how to do that. Also none of that is Fabrik specific, just responsive Joomla stuff.
2) Either override and modify your site template and/or the Fabrik list template to house the code for the changes. You will probably need the element type and class or id, which you can get in most modern browsers by right clicking it and selecting inspect element or hitting F12 in the browser and then clicking the element.
Dale