BrowserSynchronizationTimeOut is the time TP will wait for the browser busy state.
If you are trying to see if the browser actually exists than you need to use the tpAttachNoWait flag to avoid a playback error when the browser does not actually exist.
If you are trying to see if the browser is busy then there are two reliable ways that I can think of. The first is that you have to instantiate an instance of the browser so that you can access it's properties. One of the properties of an IE object is "Busy" which returns a bool as to if the browser is busy or not. IE requires that a calling object must have instantiated it.
The second which may be a little easier for you is to use the DOM. Using any HTML object you can get a document which allows you to get the "ReadyState" as in the following which uses a referrence to the Microsoft HTML library.
<font class="small">Code:</font><hr /><pre>
Dim hb As HTMLButtonElement
Dim doc As HTMLDocument
Set hb = HTMLButton("Name=textcont").Object
Set doc = hb.Document
Edited because of my awful writing skills [img]/images/graemlins/frown.gif[/img]