When is the best time to send an email to a professor about a masters position?
In the past, I tried to optimally-time emails in this fashion. I found that it usually turned into delaying the email and needing to spend mental bandwidth tracking and remembering to do that for part of a week (to the detriment of some other small tasks).

My recommendation at this point would be: Right now. As soon as you have time to do so. Get it off your plate and move on. 

Edit: I'm aware that among millennials, it's common to have email tied into one's mobile device, and therefore interact with it and view it identically to instant messaging (e.g., I've had one younger friend express irritation at receiving work emails after 5 pm). However, I will suggest that this is not the case for academics. We're usually getting hundreds of emails per week or day, and necessarily deal with it in a batched fashion at various times of our choosing (not necessarily every day).