Auto load shipping methods on lite_checkout.js file

cs-cart 4.15.2
Can someone help me how to revise the lite_checkout.js file so it auto-refreshes the shipping methods when someone types his postal code? “$zipCode”

I have set different shipping costs based on Postal Codes, so the idea is to change the displayed shipping cost when the Postal code changes.

PS: I don’t want to be a drop-down list as the postal codes are too many (I have implemented this auto refresh when someone changes the country that is a drop-down list)

Try to do it through tariff zones

I have already applied the tariff zones and they work correctly. What I need is to not have to press the button and autoload the results.
Actually, I have almost achieved that but I have this issue:
When I add this code:
$city.on('change', function (e, extra) .....

It doesn’t let me type in the field, but when I paste something in the field, it works and autoloads as I want.
So if it is a drop-down list and you choose something it works. But I don’t want a drop-down list, I want to type, and when the customer finishes typing then it autoloads