The JS code within the authorization callback is executed upon click of the button. So you could do something like this:
var authRequest;
OffAmazonPayments.Button("AmazonPayButton", "YOUR_SELLER_ID_HERE", {
type: "PwA",
color: "Gold",
size: "medium",
useAmazonAddressBook: true,
authorization: function() {
// additional on click code
_gaq.push(['_trackEvent', 'Category', 'Action', 'Extra Label if you like!']);
var loginOptions = {scope: 'profile payments:widget'};
authRequest = amazon.Login.authorize(loginOptions, "YOUR_REDIRECT_URL_HERE");
},
onError: function(error) {
// Write your custom error handling
}
});