Adding listeners to elements inside JavaScript module

I learn the design patterns for Javascript modules and I need your advice.

For example I have a js module in one file and onload file. Should I add an elements and listen events like this:

module.js

var Module = (function() {
    var obj = {};
    var _but;
    obj.addElement = function(button, callback) {
        _but.onclick = function() { callback() }
    }
    return obj;
});

init.js

window.onload = function() {
    var m = new Module();
    m.addElement(document.getElementById("but"), function() {
        alert("Do work");
    });
}

or should I add events outside the module

module.js

var Module = (function() {
    var obj = {};
    obj.doWork = function() {
        alert("Do work");
    }
    return obj;
});

init.js

window.onload = function() {
    var m = new Module();
    var but = document.getElementById("but");
    but.onclick = function() {
        m.doWork();
    }
}

I know this question looks weird, don't blame me, but I need your advice. Thank you.