JQuery / JavaScript - trigger button click from another button click event

jQuery("input.first").click(function(){
   jQuery("input.second").trigger("click");
   return false;
});

You mean this:

jQuery("input.first").click(function(){
   jQuery("input.second").trigger('click');
   return false;
});

Add id's to both inputs, id="first" and id="second"

//trigger second button
$("#second").click()

Well, you just fire the desired click event:

$(".first").click(function(){
    $(".second").click(); 
    return false;
});

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