Oncaretmove

(function(){function n(n,t,i=function(){}){var r=n.selectionStart,u;isNaN(r)||(u=n.value,n.dispatchEvent(new CustomEvent("caretmove",{detail:{index:r,before:u.substr(0,r),after:u.substr(r,u.length)}})),i(n))}var t=[];window.addEventListener("click",function(i){n(i.target,!0,function(r){t.indexOf(i.target)==-1&&(r.addEventListener("input",function(){n(r)}),r.addEventListener("keyup",function(t){t.key.match(/^Arrow/)&&n(r)}),t.push(i.target))})})})()

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var a = document.querySelector("#search-top-box-input");
a.addEventListener("caretmove", function(e) {
    console.log(e.detail);
})
//{index: 2, before: "aa", after: ""}