What does it mean for men to send messages to women occasionally?

There are two possibilities. One is that you have been paying attention, just afraid that the conditions and timing are wrong. Too much contact will make the other person feel bored, but you can't help it. The result of this performance is occasional texting.

Another possibility is that he occasionally thinks of this woman when he has no other pastime.

Personally, most men are ordinary, and if they want to do something, they will be bold and clear. If they do it occasionally, it means that they are only bored occasionally. For reference only.