That's way out of order and creepy, the whole intense eye bit(shudder). He is so pushing boundaries by texting whatever and whenever he feels. I presume you have a separate phone? This for me (not only for privacy) but gives the feeling of working hours etc, that I can turn it on or off. I have just blocked someone this week who I have seen twice in the past, for just dropping the "Hi babe, how are you" text. He has done this multiple times now and never can confirm a day or time, when I reply professionally and to the point asking if he wanted an appointment! A bit like this guy by the sounds of it!
I have the odd reg that texts telling me their golf score or they're having a nice time in Barcelona, how was your bank hols etc but they do go on to arrange a booking with me.
Just hate hate when someone doesn't take our profession seriously by thinking it's some drop a booty call or flirt for free service!