The widget can be automatically opend in combination of certain triggers. The javascript to open the widget can be found here. To inject the script into an HTML website or a Tag Manager often times it is needed to add a <script> tag before and close </script> it after.

(function() {  
var openEveryDays = 1; // widget will be open once every given days
var openBetween = ['00:00', '24:00']; // widget will be open only during this interval; UTC times
function f() {    
try {      
var LS = window.localStorage, A = window.amazd, key = 'amazd_auto_open_widget';      
var now = new Date(), iNow = +now, iLastOpen = parseInt(LS.getItem(key) || '0', 10);      
if (isNaN(iLastOpen)) iLastOpen = 0;      
if (!f.ts) f.ts = iNow; if ((iNow - f.ts) > 30000) return;      
if (!A || typeof A.maximize !== 'function') return setTimeout(f, 100);      
if ((iNow - iLastOpen) < openEveryDays * 24 * 3600 * 1000) return;      
var t = now.toISOString().split('T')[1].slice(0, 5);      
if (t < openBetween[0] || t > openBetween[1]) return;      
if (document.hidden) return;      
A.maximize();    
LS.setItem(key, iNow.toString());    
}
catch(e) {}  
}  
f();
})();