I really don't understand the "on" purpose, at all. Is it for relationships or business? I guess there is some distinction that some may find comforting (is that the right word) between the knowledge that someone hasn't read their message vs hasn't responding? Does it really make a difference? In all likeliness, the person A) saw who the message was from, and hasn't answered, or B) Saw both who the message is from, and the general content of the message from the preview, and still didn't respond. What is the real difference?
According to a stat I saw in The Guardian, most people see the text message within 90 seconds, I always respond quickly, or within a reasonable time frame, unless in certain cases, where the behavior is being mirrored between two parties, but almost always, it's so trite and petty to not respond, but people don't respond for a variety of reasons, and in many cases aren't being malicious.