Your client wants to be able to communicate with you? How dare they!
I'm not sure I understand why this is something you should be compensated for outside of the gig itself. Communication is a basic part of any business relationship.
You are a freelancer. Yes, that means you have the freedom to schedule your day. It does not mean, however, you can completely disappear and ignore your client's team just because you'd rather work at night. That's unprofessional.