How long should I wait before sending a second message?

Archive the message, saying that the owner didn't respond. They can still get back to you and vice versa, even though the message has been archived. This way you are not negatively affected in searches because of an unanswered request. Rover encourages owners to contact and interview several prospective sitters before choosing one. It could be that this particular owner is setting up meets and may get around to you at some point. The archiving doesn't affect their ability to contact and resurrect communications. You can message them again, showing your interest and availability, and then move on.

24 hours and send another text to the owner, and then if you don't hear back within a few hours I would archive the booking request so it clears up your calendar. Many owners contact several sitters so you may not hear back from them, yes its rude, but it happens often