I see him several days a week. Don't really feel the need for text "conversations" between times and am certainly not about to start trying to have important conversations by text.
However, he does sometimes send me a news article, picture or some comment about what's happening in his day. I'll respond showing some interest and he won't even look at the message for hours, then when he does often doesn't respond. .
Part of me thinks that's OK, we'll talk about it tonight/tomorrow and I don't "need" to hear from him at all. It's nice that he thought of me when he saw the article etc. Otoh why bother if you're not going to engage?