The code behind the GUI can be arbitrarily obscure. The only reliable way to understand its meaning in a general case is to run it and look at the rendered image. Trying to build a model that implicitly develops an alternative implementation of a browser inside of it sounds worse that just using an existing browser directly.

More often than not you don't have access to the underlying code, or the vendor has interest against you being able to automate it since the complexity is a part of their business model.