I have only used Live Chat with Customer Support, and never Technical Support. In all of my cases, the use was during the day. Half of the year, I am on Pacific Time, and then on Mountain Time, but that is only 1 hour difference, half the year.
I have never had an issue.
I have no answer for you, but perhaps you should call either C/S, or T/S, depending on who you wish to chat with.