Dispute grade penalty for reading in class?

I am in an large, entry level course targeted at engineers. A few weeks ago, I was reading for another class while my professor covered material I was familiar with, and she marked me down as absent for at least one and maybe two classes. She has a strict attendance policy so that she gives a 5 percent penalty for missing three or more classes, and I already have three marked absences.

The only relevant section in the syllabus says, "Good manners provide the foundation for proper classroom behavior: arrive on time, listen attentively and take detailed notes, remain quietly in your seat until dismissed by the instructor." There is a strict no-screen policy, but nothing about reading.

I am considering taking it up the ladder and arguing that she should have asked me to put the book away if she wanted me to, as I spoke to her multiple times between the time of the alleged offense and becoming aware that she had penalized me for it. Do I have a good chance of a grade appeal? on merit? statistically?

She is a teaching only professor, so I assume she doesn't have huge sway in the department. It is a ginormous class at a large school though, so I probably don't either.

The only relevant section in the syllabus says, "Good manners provide the foundation for proper classroom behavior: arrive on time, listen attentively and take detailed notes, remain quietly in your seat until dismissed by the instructor." There is a strict no-screen policy, but nothing about reading.

I am pretty sure that all department chairs would agree with a faculty member who concluded that reading in class is the opposite of listen attentively and take detailed notes. I would put your chances at exactly zero that the chair would override the decision to not credit you with attendance on that day, but marking you as absent for two days does not seem justified unless there is another penalty for not following proper classroom behavior.