"Tomorrow morning?" he suggests. It's not like he has work. Doing something useful might also calm the weird feeling of being home on a work day. People are generally too busy to entertain him that time of day.

"Also," he adds, before Sherlock thinks it's time to move on. "Can you tell me anything about him? Like, friends, family, work, that kind of thing?"

One of the reasons he got absolutely nowhere with Turner back in that basement felt like it was because he had zero handholds, zero knowledge to base himself off. So it's important not just for him to get a better idea of who Turner is for his own sake, but if he's going to try to talk to him.