You'd be better of spending your time getting mentions for the business in the local newspapers, blogs, etc with a link back to the site associated with the listing if building local authority is your goal. Adding social links to your GMB is not going to do anything for you, unless you want people to hit up your social pages.
Why do you want people to visit FB or whatever? If they have searched for something local then they are ready to pick up the phone. Your profile should be enough to do this. Itβs like putting you social links on your website - pointless. You want people to come from FB not go to FB.
I checked with some friends and no one has seen this before for auto dealers. It has been seen for malls and shopping centers though, which makes me wonder about your categories... What categories do you have set for the Lewis Ford of Hays listing?