If a guy is interested in a girl, would he go a few days without messaging her on his own?

if a guy is interested in a girl, would he go a few days without messaging her, even if he is active on that messaging app? Do guys sometimes go a bit without messaging you to see if you will message him first or care that you guys aren't talking, even if you guys aren't dating but he is interested in you?

If a guy is interested in a girl, would he go a few days without messaging her on his own?
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