The script tracks search experiences that update automatically as you type. Known as Incremental Search in software and As-You-Type in web applications. This solution offers a way to track the value as a timeout expires after keypress. There is logic to prevent redundant events from firing.

Tracking Incremental Search.js

/* 
 * Based on example at https://developer.mozilla.org/en-US/docs/Web/API/WindowOrWorkerGlobalScope/clearTimeout 
 * Usage: edit config variables, copy+paste into JS console, type in search field and wait for dataLayer push
 */

(function(dL) {
    
    /*
     * Application Functions
     */
    var delay = 2000,  // 2 second timeout
        selector = "input[type=search]",   // CSS selector for search field
        verb = "keyup",    // event listener, reference: https://developer.mozilla.org/en-US/docs/Web/Events
        searchTimer = {  
            sendData: function(query) {  // 'query' is result of the CSS selector
                this.timeoutID = undefined;    
                dL.push({"event": "search-term", "search-value": query}) // dataLayer object push
            },
            setup: function(query) {     
                if (typeof this.timeoutID === 'number') {
                    this.cancel(); // clearout existing timer, prevents multiple events from being pushed
                }
                this.timeoutID = window.setTimeout(function(query) {
                    this.sendData(query);  // we hit the delay timeout, send data!
                }.bind(this), delay, query);
            },
            cancel: function() {    // used to prevent multiple dataLayer pushes per delay period
                window.clearTimeout(this.timeoutID);
                this.timeoutID = undefined;
            }
        };
    
    /*
     * Measurement Logic
     */
    document.querySelectorAll(selector).forEach(function(input) {   // loop through all matching search fields
        input.addEventListener(verb, function(element) {   // attach the event listener to each element
            searchTimer.setup(element.target.value);   // setup begins or resets the timer, input search term
        });
    });
    
})(window.dataLayer = window.dataLayer || [])  // init dataLayer to prevent collisions