Send a message.
Presumably new messages go to the top of the queue. So when is the best day/time to send a message in the hope of it actually being read
I honestly don't know the answer to that ,late at night is when I seem to get more so maybe not then.
Just go for it anyway,if you're what they're after you're more likely to get a reply anytime .
Their isn't a best time because you never know how many messages they are receiving at the time you may be sending. So send and be patient if it gets read and no reply might be not interested