Hide Chat Option for Timeout

I very much like the new timeout feature added recently, but there is one more change/addition I would like to see to use on my community. I would like an option to make it so users in timeout cannot see chat. This is our preferred level of muting on our community and without that capability with the timeout feature, we have decided to stick with a muted role rather than adopting timeouts. I would love to see an option at the very least with the timeout feature to hide chats from users in time out.