The connection timeout would start when you make this call:
response, content = http.request( proxyConnectURL,
It is independent of whether you are logged in at remot3.it.
Is it the same method? Well yes and no, the URL:port retrieved from our servers is the same API being used. However, the web page code and the Python code have nothing to do with each other.
By the way, thanks for your interest in this code, I am reliving memories of testing it at Starbucks. 8^)